Groups and geometric analysis: integral geometry, invariant differential operators, and spherical functions
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Soc.
2002
|
| Edition: | Reprinted with corr. |
| Series: | Mathematical surveys and monographs
83 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 667 S. |
| ISBN: | 0821826735 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV023345062 | ||
| 003 | DE-604 | ||
| 005 | 20230911 | ||
| 007 | t | ||
| 008 | 080616s2002 |||| 00||| eng d | ||
| 020 | |a 0821826735 |9 0-8218-2673-5 | ||
| 035 | |a (OCoLC)249534308 | ||
| 035 | |a (DE-599)BVBBV023345062 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-703 | ||
| 084 | |a SK 340 |0 (DE-625)143232: |2 rvk | ||
| 084 | |a SK 370 |0 (DE-625)143234: |2 rvk | ||
| 100 | 0 | |a Sigurður Helgason |d 1927-2023 |e Verfasser |0 (DE-588)123045762 |4 aut | |
| 245 | 1 | 0 | |a Groups and geometric analysis |b integral geometry, invariant differential operators, and spherical functions |c Sigurdur Helgason |
| 250 | |a Reprinted with corr. | ||
| 264 | 1 | |a Providence, RI |b American Mathematical Soc. |c 2002 | |
| 300 | |a XXII, 667 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v 83 | |
| 650 | 0 | 7 | |a Invarianter Differentialoperator |0 (DE-588)4162210-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kugelfunktion |0 (DE-588)4033494-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integralgeometrie |0 (DE-588)4161911-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Integralgeometrie |0 (DE-588)4161911-0 |D s |
| 689 | 0 | 1 | |a Invarianter Differentialoperator |0 (DE-588)4162210-8 |D s |
| 689 | 0 | 2 | |a Kugelfunktion |0 (DE-588)4033494-6 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Invarianter Differentialoperator |0 (DE-588)4162210-8 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Kugelfunktion |0 (DE-588)4033494-6 |D s |
| 689 | 2 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1310-1 |
| 830 | 0 | |a Mathematical surveys and monographs |v 83 |w (DE-604)BV000018014 |9 83 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016528766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016528766 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804137699902226432 |
|---|---|
| adam_text | CONTENTS
Preface
.................................. xiii
Preface to the
2000
Printing
.......................... xvii
Suggestions to the Reader
......................... xix
A Sequel to the Present Volume
........................ xxi
INTRODUCTION
Geometric Fourier Analysis on Spaces of Constant Curvature
1.
Harmonic Analysis on Homogeneous Spaces
................ 1
1.
General Problems
.......................... 1
2.
Notation and Preliminaries
...................... 2
2.
The Euclidean Plane R1
......................... 4
Λ
Eigenfunctions and
Eigenspace
Representations
.............. 4
2.
Λ
Theorem of Paley-Wiener Type
................... 15
3.
The Sphered
............................. 16
/.
Spherical Harmonics
......................... 16
2.
Proof of Theorem
2.10........................ 23
4.
The Hyperbolic Plane H2
........................ 29
1.
Non-Euclidean Fourier Analysis. Problems and Results
.......... 29
2.
The Spherical Functions and Spherical Transforms
............ 38
3.
The Non-Euclidean Fourier Transform. Proof of the Main Result
...... 44
4.
Eigenfunctions and
Eigenspace
Representations. Proofs of
Theorems
4.3
and
4.4........................ 58
5.
Limit Theorems
........................... 69
Exercises and Further Results
..................... 72
Notes
............................... 78
CHAPTER I
Integral Geometry and Radon Transforms
1.
Integration on Manifolds
........................ 81
/.
integration of Forms. Riemannian Measure
............... 81
2.
Invariant Measures on Coset Spaces
.................. 85
3. Haar
Measure in Canonical Coordinates
................ 96
2.
The Radon Transform on R
....................... 96
/.
introduction
............................ 96
2.
The Radon Transform of the Spaces SiR ) and
<f(fí ).
The Support Theorem
........................ 97
vii
viii CONTENTS
3.
The Inversion Formulas
........................
HO
4.
The
Fiancherei
Formula
....................... 115
5.
The Radon Transform of Distributions
................. 117
6.
integration over d-Planes.
Х
-Ray Transforms
.............. 122
7.
Applications
............................ 126
A. Partial Differential Equations
................... 126
B. Radiography
.......................... 130
8.
Appendix. Distributions and Riesz Potentials
............... 131
3.
A Duality in Integral Geometry. Generalized Radon Transforms
and Orbital Integrals
.......................... 139
1.
A Duality for Homogeneous Spaces
.................. 139
2.
The Radon Transform for the Double Fibration
.............. 143
3.
Orbital Integrals
.......................... 149
4.
The Radon Transform on Two-Point Homogeneous Spaces.
The X-Ray Transform
.......................... 150
/.
Spaces of Constant Curvature
..................... 151
A. The Hyperbolic Space
...................... 152
B. The Spheres and the Elliptic Spaces
................ 161
2.
Compact Two-Point Homogeneous Spaces
................ 164
3.
Noncompact Two-Point Homogeneous Spaces
.............. 177
4.
The
Х
-Ray Transform on a Symmetric Space
.............. 178
5.
Integral Formulas
........................... 180
1. Integral Formulas Related to the Iwasawa Decomposition
......... 181
2.
Integral Formulas for the
Carian
Decomposition
............. 186
A. The Noncompact Case
...................... 186
B. The Compact Case
....................... 187
С
The Lie Algebra Case
...................... 195
3.
Integral Formulas for the Bruhat Decomposition
............. 196
6.
Orbital Integrals
............................ 199
1.
Pseudo-Riemannian Manifolds of Constant Curvature
........... 199
2.
Orbital Integrals for the Lorentzian Case
................ 203
3.
Generalized Riesz Potentials
..................... 211
4.
Determination of a Function from Its Integrals over Lorentzian Spheres
. . . 214
5.
Orbital Integrals on SL(2,R)
..................... 218
Exercises and Further Results
...................... 221
Notes
................................. 229
CHAPTER II
Invariant Differential Operators
1.
Differentiable Functions on R
...................... 233
2.
Differential Operators on Manifolds
.................... 239
1. Definition. The Spaces 3i{M) and <Z(M)
................. 239
2.
Topology of the Spaces
ЗЦМ)
and ${M). Distributions
........... 239
3.
Effect of Mappings. The Adjoint
.................... 241
4.
The Laplace-
Belframi
Operator
.................... 242
3.
Geometric Operations on Differential Operators
.............. 251
Л
Projections of Differential Operators
.................. 251
2.
Transversal Parts and Separation of Variables for Differential Operators
. . . 253
CONTENTS
IX
3.
Radial Parts
of a Differential Operator.
General
Theory
.......... 259
4.
Examples of
Radia! Parts
....................... 265
4.
Invariant Differential Operators on Lie Groups and Homogeneous Spaces
. . . 274
Λ
Introductory Remarks. Examples. Problems
............... 274
2.
The Algebra D(GIH)
......................... 280
3.
The Case of
α
Two-Point Homogeneous Space. The Generalized
Darboux Equation
.......................... 287
5.
Invariant Differential Operators on Symmetric Spaces
............ 289
/.
The Action on Distributions and Commutativity
............. 289
2.
The Connection with Weyl Group Invariants
............... 295
3.
The Polar Coordinate Form of the Laplacian
................ 309
4.
The Laplace-Beltrami Operator for a Symmetric Space ofRank One
.... 312
5.
The
Poisson
Equation Generalized
................... 315
6.
Asgeirsson s Mean-Value Theorem Generalized
.............. 318
7.
Restriction of the Central Operators in D{G)
............... 323
8.
Invariant Differential Operators for Complex
Semisimple
Lie Algebras
.... 326
9.
Invariant Differential Operators for X
-
GjK,
G
Complex
......... 329
Exercises and Further Results
...................... 330
Notes
................................. 343
CHAPTER III
Invariants and Harmonic Polynomials
1.
Decomposition of the Symmetric Algebra. Harmonic Polynomials
....... 345
2.
Decomposition of the Exterior Algebra. Primitive Forms
........... 354
3.
Invariants for the Weyl Group
...................... 356
1.
Symmetric Invariants
........................ 356
2.
Harmonic Polynomials
........................ 360
3.
The Exterior Invariants
......................... 363
4.
Eigenfunctions of Weyl Group Invariant Operators
............ 364
5.
Restriction Properties
........................ 366
4.
The Orbit Structure of
ρ
......................... 368
ƒ.
Generalities
............................ 368
2. Nilpotent
Elements
......................... 370
3.
Regular Elements
.......................... 373
4. Semisimple
Elements
......................... 378
5.
Algebro-Geometric Results on the Orbits
................ 380
5.
Harmonic Polynomials on
ρ
....................... 380
Exercises and Further Results
...................... 382
Notes
................................. 384
CHAPTER IV
Spherical Functions and Spherical Transforms
1.
Representations
............................ 385
1. Generalities
............................ 385
2.
Compact Groups
.......................... 390
χ
CONTENTS
2.
Spherical Functions: Preliminaries
.................... 399
ƒ.
Definition
............................. 399
2.
Joint Eigenfunctions
......................... 402
3.
Examples
............................. 403
3.
Elementary Properties of Spherical Functions
................ 407
4.
Integral Formulas for Spherical Functions. Connections with Representations
. . 416
1.
The Compact Type
......................... 416
2.
The Noncompact Type
........................ 417
3.
The Euclidean Type
......................... 424
5.
Harish-Chandra s Spherical Function Expansion
.............. 425
/.
The General Case
.......................... 425
2.
The Complex Case
......................... 432
6.
The c-Function
............................. 434
1.
The Behavior of
ψλ
at oo
....................... 434
2.
The Rank-One Case
......................... 436
3.
Properties of H(n)
.......................... 438
4.
Integrals of
Nilpotent
Groups
..................... 439
5.
The Weyl Group Acting on the Root System
............... 441
6.
The Rank-One Reduction. The Product Formula of Gindikin-Karpelevib
. . . 444
7.
The Paley-Wiener Theorem and the Inversion Formula for the
Spherical Transform
.......................... 448
/.
Normalization of Measures
...................... 449
2.
The Image
ofíŕifi)
under the Spherical Transform,
The Paley- Wiener Theorem
...................... 450
3.
The Inversion Formula
........................ 454
8.
The Bounded Spherical Functions
..................... 458
/.
Generalities
............................ 458
2.
Convex Hulls
............................ 459
3.
Boundary Components
........................ 461
9.
The Spherical Transform on p, the Euclidean Type
............. 467
10.
Convexity Theorems
.......................... 472
Exercises and Further Results
...................... 481
Notes
................................. 491
CHAPTER V
Analysis on Compact Symmetric Spaces
Representations of Compact Lie Groups
.................. 495
/.
The Weights
............................ 496
2.
The Characters
........................... 501
Fourier Expansions on Compact Groups
.................. 507
1.
Introduction. L K) versus
L2(K)
.................... 507
2.
The Circle Group
.......................... 508
3.
Spectrally Continuous Operators
.................... 510
4.
Absolute Convergence
........................ 519
5.
Імсипагу
Fourier Series
....................... 522
Fourier Decomposition of a Representation
................ 529
/.
Generalities
............................ 529
2.
Applications to Compact Homogeneous Spaces
.............. 532
CONTENTS
ХІ
4.
The Case of a Compact Symmetric Space
................. 534
1.
Finite-Dimensional Spherical Representations
.............. 534
2.
The Eigenfunctions and the
Eigenspace
Representations
.......... 538
3.
The Rank-One Case
......................... 542
Exercises and Further Results
...................... 543
Notes
................................. 548
Solutions to Exercises
........................... 551
Appendix
................................. 597
1. The Finite-Dimensional Representations ofs!(2,C)
............. 597
2.
Representations and Reductive Lie Algebras
................ 600
/. Semisimple
Representations
...................... 600
2. Nilpotent
and
Semisimple
Elements
................... 602
3.
Reductive Lie Algebras
........................ 605
3.
Some Algebraic Tools
.......................... 607
Some Details
................................. 611
Bibliography
............................... 619
Symbols Frequently Used
......................... 655
Index
................................... 659
Errata
................................... 665
|
| adam_txt |
CONTENTS
Preface
. xiii
Preface to the
2000
Printing
. xvii
Suggestions to the Reader
. xix
A Sequel to the Present Volume
. xxi
INTRODUCTION
Geometric Fourier Analysis on Spaces of Constant Curvature
1.
Harmonic Analysis on Homogeneous Spaces
. 1
1.
General Problems
. 1
2.
Notation and Preliminaries
. 2
2.
The Euclidean Plane R1
. 4
Λ
Eigenfunctions and
Eigenspace
Representations
. 4
2.
Λ
Theorem of Paley-Wiener Type
. 15
3.
The Sphered
. 16
/.
Spherical Harmonics
. 16
2.
Proof of Theorem
2.10. 23
4.
The Hyperbolic Plane H2
. 29
1.
Non-Euclidean Fourier Analysis. Problems and Results
. 29
2.
The Spherical Functions and Spherical Transforms
. 38
3.
The Non-Euclidean Fourier Transform. Proof of the Main Result
. 44
4.
Eigenfunctions and
Eigenspace
Representations. Proofs of
Theorems
4.3
and
4.4. 58
5.
Limit Theorems
. 69
Exercises and Further Results
. 72
Notes
. 78
CHAPTER I
Integral Geometry and Radon Transforms
1.
Integration on Manifolds
. 81
/.
integration of Forms. Riemannian Measure
. 81
2.
Invariant Measures on Coset Spaces
. 85
3. Haar
Measure in Canonical Coordinates
. 96
2.
The Radon Transform on R"
. 96
/.
introduction
. 96
2.
The Radon Transform of the Spaces SiR") and
<f(fí").
The Support Theorem
. 97
vii
viii CONTENTS
3.
The Inversion Formulas
.
HO
4.
The
Fiancherei
Formula
. 115
5.
The Radon Transform of Distributions
. 117
6.
integration over d-Planes.
Х
-Ray Transforms
. 122
7.
Applications
. 126
A. Partial Differential Equations
. 126
B. Radiography
. 130
8.
Appendix. Distributions and Riesz Potentials
. 131
3.
A Duality in Integral Geometry. Generalized Radon Transforms
and Orbital Integrals
. 139
1.
A Duality for Homogeneous Spaces
. 139
2.
The Radon Transform for the Double Fibration
. 143
3.
Orbital Integrals
. 149
4.
The Radon Transform on Two-Point Homogeneous Spaces.
The X-Ray Transform
. 150
/.
Spaces of Constant Curvature
. 151
A. The Hyperbolic Space
. 152
B. The Spheres and the Elliptic Spaces
. 161
2.
Compact Two-Point Homogeneous Spaces
. 164
3.
Noncompact Two-Point Homogeneous Spaces
. 177
4.
The
Х
-Ray Transform on a Symmetric Space
. 178
5.
Integral Formulas
. 180
1. Integral Formulas Related to the Iwasawa Decomposition
. 181
2.
Integral Formulas for the
Carian
Decomposition
. 186
A. The Noncompact Case
. 186
B. The Compact Case
. 187
С
The Lie Algebra Case
. 195
3.
Integral Formulas for the Bruhat Decomposition
. 196
6.
Orbital Integrals
. 199
1.
Pseudo-Riemannian Manifolds of Constant Curvature
. 199
2.
Orbital Integrals for the Lorentzian Case
. 203
3.
Generalized Riesz Potentials
. 211
4.
Determination of a Function from Its Integrals over Lorentzian Spheres
. . . 214
5.
Orbital Integrals on SL(2,R)
. 218
Exercises and Further Results
. 221
Notes
. 229
CHAPTER II
Invariant Differential Operators
1.
Differentiable Functions on R"
. 233
2.
Differential Operators on Manifolds
. 239
1. Definition. The Spaces 3i{M) and <Z(M)
. 239
2.
Topology of the Spaces
ЗЦМ)
and ${M). Distributions
. 239
3.
Effect of Mappings. The Adjoint
. 241
4.
The Laplace-
Belframi
Operator
. 242
3.
Geometric Operations on Differential Operators
. 251
Л
Projections of Differential Operators
. 251
2.
Transversal Parts and Separation of Variables for Differential Operators
. . . 253
CONTENTS
IX
3.
Radial Parts
of a Differential Operator.
General
Theory
. 259
4.
Examples of
Radia! Parts
. 265
4.
Invariant Differential Operators on Lie Groups and Homogeneous Spaces
. . . 274
Λ
Introductory Remarks. Examples. Problems
. 274
2.
The Algebra D(GIH)
. 280
3.
The Case of
α
Two-Point Homogeneous Space. The Generalized
Darboux Equation
. 287
5.
Invariant Differential Operators on Symmetric Spaces
. 289
/.
The Action on Distributions and Commutativity
. 289
2.
The Connection with Weyl Group Invariants
. 295
3.
The Polar Coordinate Form of the Laplacian
. 309
4.
The Laplace-Beltrami Operator for a Symmetric Space ofRank One
. 312
5.
The
Poisson
Equation Generalized
. 315
6.
Asgeirsson's Mean-Value Theorem Generalized
. 318
7.
Restriction of the Central Operators in D{G)
. 323
8.
Invariant Differential Operators for Complex
Semisimple
Lie Algebras
. 326
9.
Invariant Differential Operators for X
-
GjK,
G
Complex
. 329
Exercises and Further Results
. 330
Notes
. 343
CHAPTER III
Invariants and Harmonic Polynomials
1.
Decomposition of the Symmetric Algebra. Harmonic Polynomials
. 345
2.
Decomposition of the Exterior Algebra. Primitive Forms
. 354
3.
Invariants for the Weyl Group
. 356
1.
Symmetric Invariants
. 356
2.
Harmonic Polynomials
. 360
3.
The Exterior Invariants
. 363
4.
Eigenfunctions of Weyl Group Invariant Operators
. 364
5.
Restriction Properties
. 366
4.
The Orbit Structure of
ρ
. 368
ƒ.
Generalities
. 368
2. Nilpotent
Elements
. 370
3.
Regular Elements
. 373
4. Semisimple
Elements
. 378
5.
Algebro-Geometric Results on the Orbits
. 380
5.
Harmonic Polynomials on
ρ
. 380
Exercises and Further Results
. 382
Notes
. 384
CHAPTER IV
Spherical Functions and Spherical Transforms
1.
Representations
. 385
1. Generalities
. 385
2.
Compact Groups
. 390
χ
CONTENTS
2.
Spherical Functions: Preliminaries
. 399
ƒ.
Definition
. 399
2.
Joint Eigenfunctions
. 402
3.
Examples
. 403
3.
Elementary Properties of Spherical Functions
. 407
4.
Integral Formulas for Spherical Functions. Connections with Representations
. . 416
1.
The Compact Type
. 416
2.
The Noncompact Type
. 417
3.
The Euclidean Type
. 424
5.
Harish-Chandra's Spherical Function Expansion
. 425
/.
The General Case
. 425
2.
The Complex Case
. 432
6.
The c-Function
. 434
1.
The Behavior of
'ψλ
at oo
. 434
2.
The Rank-One Case
. 436
3.
Properties of H(n)
. 438
4.
Integrals of
Nilpotent
Groups
. 439
5.
The Weyl Group Acting on the Root System
. 441
6.
The Rank-One Reduction. The Product Formula of Gindikin-Karpelevib
. . . 444
7.
The Paley-Wiener Theorem and the Inversion Formula for the
Spherical Transform
. 448
/.
Normalization of Measures
. 449
2.
The Image
ofíŕifi)
under the Spherical Transform,
The Paley- Wiener Theorem
. 450
3.
The Inversion Formula
. 454
8.
The Bounded Spherical Functions
. 458
/.
Generalities
. 458
2.
Convex Hulls
. 459
3.
Boundary Components
. 461
9.
The Spherical Transform on p, the Euclidean Type
. 467
10.
Convexity Theorems
. 472
Exercises and Further Results
. 481
Notes
. 491
CHAPTER V
Analysis on Compact Symmetric Spaces
Representations of Compact Lie Groups
. 495
/.
The Weights
. 496
2.
The Characters
. 501
Fourier Expansions on Compact Groups
. 507
1.
Introduction. L\K) versus
L2(K)
. 507
2.
The Circle Group
. 508
3.
Spectrally Continuous Operators
. 510
4.
Absolute Convergence
. 519
5.
Імсипагу
Fourier Series
. 522
Fourier Decomposition of a Representation
. 529
/.
Generalities
. 529
2.
Applications to Compact Homogeneous Spaces
. 532
CONTENTS
ХІ
4.
The Case of a Compact Symmetric Space
. 534
1.
Finite-Dimensional Spherical Representations
. 534
2.
The Eigenfunctions and the
Eigenspace
Representations
. 538
3.
The Rank-One Case
. 542
Exercises and Further Results
. 543
Notes
. 548
Solutions to Exercises
. 551
Appendix
. 597
1. The Finite-Dimensional Representations ofs!(2,C)
. 597
2.
Representations and Reductive Lie Algebras
. 600
/. Semisimple
Representations
. 600
2. Nilpotent
and
Semisimple
Elements
. 602
3.
Reductive Lie Algebras
. 605
3.
Some Algebraic Tools
. 607
Some Details
. 611
Bibliography
. 619
Symbols Frequently Used
. 655
Index
. 659
Errata
. 665 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Sigurður Helgason 1927-2023 |
| author_GND | (DE-588)123045762 |
| author_facet | Sigurður Helgason 1927-2023 |
| author_role | aut |
| author_sort | Sigurður Helgason 1927-2023 |
| author_variant | s h sh |
| building | Verbundindex |
| bvnumber | BV023345062 |
| classification_rvk | SK 340 SK 370 |
| ctrlnum | (OCoLC)249534308 (DE-599)BVBBV023345062 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Reprinted with corr. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02094nam a2200481 cb4500</leader><controlfield tag="001">BV023345062</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230911 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080616s2002 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821826735</subfield><subfield code="9">0-8218-2673-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)249534308</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023345062</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-703</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 340</subfield><subfield code="0">(DE-625)143232:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 370</subfield><subfield code="0">(DE-625)143234:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="0" ind2=" "><subfield code="a">Sigurður Helgason</subfield><subfield code="d">1927-2023</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)123045762</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Groups and geometric analysis</subfield><subfield code="b">integral geometry, invariant differential operators, and spherical functions</subfield><subfield code="c">Sigurdur Helgason</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Reprinted with corr.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Mathematical Soc.</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXII, 667 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematical surveys and monographs</subfield><subfield code="v">83</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Invarianter Differentialoperator</subfield><subfield code="0">(DE-588)4162210-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kugelfunktion</subfield><subfield code="0">(DE-588)4033494-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integralgeometrie</subfield><subfield code="0">(DE-588)4161911-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Integralgeometrie</subfield><subfield code="0">(DE-588)4161911-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Invarianter Differentialoperator</subfield><subfield code="0">(DE-588)4162210-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Kugelfunktion</subfield><subfield code="0">(DE-588)4033494-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Invarianter Differentialoperator</subfield><subfield code="0">(DE-588)4162210-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Kugelfunktion</subfield><subfield code="0">(DE-588)4033494-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4704-1310-1</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematical surveys and monographs</subfield><subfield code="v">83</subfield><subfield code="w">(DE-604)BV000018014</subfield><subfield code="9">83</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016528766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016528766</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV023345062 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:03:07Z |
| indexdate | 2024-07-09T21:16:27Z |
| institution | BVB |
| isbn | 0821826735 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016528766 |
| oclc_num | 249534308 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 |
| owner_facet | DE-355 DE-BY-UBR DE-703 |
| physical | XXII, 667 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Soc. |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Sigurður Helgason 1927-2023 Verfasser (DE-588)123045762 aut Groups and geometric analysis integral geometry, invariant differential operators, and spherical functions Sigurdur Helgason Reprinted with corr. Providence, RI American Mathematical Soc. 2002 XXII, 667 S. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 83 Invarianter Differentialoperator (DE-588)4162210-8 gnd rswk-swf Kugelfunktion (DE-588)4033494-6 gnd rswk-swf Integralgeometrie (DE-588)4161911-0 gnd rswk-swf Integralgeometrie (DE-588)4161911-0 s Invarianter Differentialoperator (DE-588)4162210-8 s Kugelfunktion (DE-588)4033494-6 s 1\p DE-604 DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1310-1 Mathematical surveys and monographs 83 (DE-604)BV000018014 83 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016528766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sigurður Helgason 1927-2023 Groups and geometric analysis integral geometry, invariant differential operators, and spherical functions Mathematical surveys and monographs Invarianter Differentialoperator (DE-588)4162210-8 gnd Kugelfunktion (DE-588)4033494-6 gnd Integralgeometrie (DE-588)4161911-0 gnd |
| subject_GND | (DE-588)4162210-8 (DE-588)4033494-6 (DE-588)4161911-0 |
| title | Groups and geometric analysis integral geometry, invariant differential operators, and spherical functions |
| title_auth | Groups and geometric analysis integral geometry, invariant differential operators, and spherical functions |
| title_exact_search | Groups and geometric analysis integral geometry, invariant differential operators, and spherical functions |
| title_exact_search_txtP | Groups and geometric analysis integral geometry, invariant differential operators, and spherical functions |
| title_full | Groups and geometric analysis integral geometry, invariant differential operators, and spherical functions Sigurdur Helgason |
| title_fullStr | Groups and geometric analysis integral geometry, invariant differential operators, and spherical functions Sigurdur Helgason |
| title_full_unstemmed | Groups and geometric analysis integral geometry, invariant differential operators, and spherical functions Sigurdur Helgason |
| title_short | Groups and geometric analysis |
| title_sort | groups and geometric analysis integral geometry invariant differential operators and spherical functions |
| title_sub | integral geometry, invariant differential operators, and spherical functions |
| topic | Invarianter Differentialoperator (DE-588)4162210-8 gnd Kugelfunktion (DE-588)4033494-6 gnd Integralgeometrie (DE-588)4161911-0 gnd |
| topic_facet | Invarianter Differentialoperator Kugelfunktion Integralgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016528766&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT sigurðurhelgason groupsandgeometricanalysisintegralgeometryinvariantdifferentialoperatorsandsphericalfunctions |