Clifford algebras in analysis and related topics:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
1996
|
| Series: | Studies in Advanced Mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 366 Seiten Ill., graph. Darst. |
| ISBN: | 0849384818 |
Staff View
MARC
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| 245 | 1 | 0 | |a Clifford algebras in analysis and related topics |c John Ryan, University of Arkansas |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC Press |c 1996 | |
| 300 | |a VII, 366 Seiten |b Ill., graph. Darst. | ||
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Record in the Search Index
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Contents
1 Acknowledgment 1
2 Conference Participants 3
3 Introduction
John Ryan 7
4 Problem Book
H. Blaine Lawson 17
5 Clifford Algebras, Fourier Theory, Singular Integrals,
and Harmonic Functions on Lipschitz Domains
Alan Mclntosh 33
5.1 Introduction 33
5.2 Lecture 1 34
5.2.1 (A) Spectral theory of £ € Rm 36
5.2.2 (B) Spectral theory of C € Cm 37
5.3 Lecture 2 40
5.3.1 (C) Spectral theory of commuting matrices 40
5.3.2 (D) Spectral theory of the Dirac operator D 43
5.4 Lecture 3 50
5.4.1 (E) Monogenic functions 50
5.4.2 (F) Singular convolution integrals on Lipschitz surfaces 56
5.5 Lecture 4 63
5.5.1 (G) Fourier transforms 63
5.5.2 (H) Correspondence between monogenic functions and
holomorphic functions of several complex variables
under Fourier transforms 67
5.6 Lecture 5 71
5.6.1 (J) Algebras of singular integrals on Lipschitz sur¬
faces, and functional calculi of Dirac operators on
these surfaces 71
5.6.2 (K) Boundary value problems for harmonic functions 75
5.7 Additional Material 78
5.7.1 (L) Singular integrals on the boundary of a strongly
Lipschitz domain 78
5.7.2 (M) More about singular convolution integrals on
Lipschitz surfaces 80
iv
6 Clifford Algebras and H^ Functional Calculi of
Commuting Operators
Chun Li and Alan Mclntosh 89
6.1 Introduction 89
6.2 The Hoc functional calculus of a single operator 89
6.3 Fourier transform between holomorphic functions and mono
genic functions 92
6.4 Hqo functional calculi of n tuples of commuting operators . 97
7 Hypercomplex Variable Techniques in
Harmonic Analysis
Marius Mitrea 103
7.1 Introduction 103
7.2 Clifford Algebra Rudiments 104
7.3 Elements of Clifford Analysis 106
7.4 Non Homogeneous Dirac Operators 108
7.5 Clifford Algebra Valued Singular Integral Operators .... 109
7.6 Hardy Spaces on Lipschitz Domains 112
7.7 Rellich Type Formulas for Monogenic Functions 120
7.8 A Burkholder Gundy Silverstein Theorem for Monogenic Func¬
tions in Lipschitz Domains 121
7.9 Some Applications to the Theory of Harmonic Functions in
Lipschitz Domains 123
8 Some Applications of Conformal Covariance in
Clifford Analysis
John Ryan 129
8.1 Introduction 129
8.2 Preliminaries 131
8.3 Conformal Invariance of Cells of Harmonicity 134
8.4 V(n) and Real Clifford Analysis 137
8.5 V (Cn) and Complex Clifford Analysis 145
8.6 The Bergman Kernel and Harmonic Measure 149
8.7 More on Conformal Covariance in Complex Clifford Analysis 153
9 Singular Integrals with Monogenic Kernels on the
m Torus and their Lipschitz Perturbations
Tao Qian 157
9.1 Introduction 157
9.2 Preliminary 159
9.3 Fourier Transforms 161
9.4 Singular Integral Operators and Fourier Multiplier Opera¬
tors on Periodic Lipschitz Surfaces 167
V
10 Scattering Theory for Orthogonal Wavelets
Palle E.T. Jorgensen 173
10.1 Introduction 173
10.2 Preliminaries 174
10.3 Scattering Theory 177
10.4 Wavelets 181
10.5 Multiresolutions 184
10.6 The Integral Translation Group 188
10.7 The Besicovich Spaces 192
11 Acoustic Scattering, Galerkin Estimates and
Clifford Algebras
Bjorn Jawerth and Marius Mitrea 199
11.1 Introduction 199
11.2 Definitions and Preliminary Results 202
11.3 Inverting Quaternionic Valued Boundary Operators 206
11.4 Finite Element Spaces 208
11.5 Local Galerkin Estimates 211
12 Clifford Algebras, Hardy Spaces, and
Compensated Compactness
Zhijian Wu 217
12.1 Introduction 217
12.2 Preliminaries 219
12.3 Components of the product of two monogenic functions . . 222
12.4 Proof of the main theorems 229
12.5 Applications in compensated compactness 236
13 Frame Decompositions of Form Valued Hardy Spaces
J.E. Gilbert, J.A. Hogan, and J.D. Lakey 239
13.1 Introduction 239
13.2 Dilatation Frames 241
13.3 The deRham complex and Hardy spaces of forms 246
13.4 Projections on H?r 250
13.5 Lusin s representation for H?r 251
13.6 Discrete frames: the case of one forms 255
13.7 Concluding remarks and problems 256
14 Applications of Clifford Analysis to Inverse Scattering
for the Linear Hierarchy in Several Space Dimensions
Daniel B. Dix 261
14.1 Introduction 261
14.2 Review of Some Clifford Analysis 262
vi
14.3 Relation between Complex and Clifford Analysis in Dimen¬
sion One 265
14.4 Review of the Linear Hierarchy in One Space Dimension . . 272
14.5 The Linear Hierarchy in Several Space Dimensions 278
15 On Riemann Hilbert Problems for Nonhomogeneous
Dirac Equations in a Half Space of Rm(m 2)
Zhenyuan Xu and Chiping Zhou 285
15.1 Introduction 285
15.2 Preliminaries 286
15.3 Riemann Hilbert Problems for Nonhomogeneous Dirac Equa¬
tions 289
16 Regularity and Approximation Results for the
Maxwell Problem on C1 and Lipschitz Domains
Marius Mitrea, Rodolfo H. Torres, and Grant V. Welland 297
16.1 Introduction 297
16.2 The vector Helmholtz equation 300
16.3 The singular integral operator M 301
16.4 Sobolev Besov space regularity results 302
16.5 Some approximation results 304
17 Continuity of Calderon Zygmund Type Operators on
the Predual of a Morrey Space
Josefina Alvarez 309
17.1 Introduction 309
17.2 Definition of the Space Lp^ 310
17.3 The Space U * as the Dual of the Atomic Space IP * ... 311
17.4 A Notion of a Molecule in the Space W^ 312
17.5 Continuity on the Spaces W f and LPV of Calderon Zygmund
Type Operators 315
18 Neumann Type Problems for the Dirac Operator
Chiping Zhou 321
18.1 Introduction 321
18.2 Neumann Problems for Monogenic Functions 323
18.3 Neumann Problems for Nonhomogeneous Dirac Equations . 328
19 The Hyperholomorphic Bergman Projector and
its Properties
E. Ramirez de Arellano, M. Shapiro, and N. Vasilevski 333
19.1 Introduction 333
19.2 Preliminaries 334
vii
19.3 The T operator and the singular integral operator over a
domain 337
19.4 Bergman hyperholomorphic spaces and Bergman hyperholo
morphic projector 338
19.5 Some algebras generated by the Bergman projector 341
20 Multivector Solutions to the Hyperholomorphic
Massive Dirac Equation
William M. Pezzaglia, Jr. 345
20.1 Introduction 345
20.2 Algebraic Notation 346
20.2.1 Classical Galilean Space and The Pauli Algebra . . . 347
20.2.2 Minkowski Spacetime and Majorana Algebra .... 347
20.2.3 Automorphisms and Conservation Laws 348
20.3 Functional Solutions of the Massive Dirac Equation 350
20.3.1 Relativistic Quantum Wave Equations 350
20.3.2 Meta Monogenic Functions 351
20.3.3 Multivectorial Hilbert Space 352
20.4 Integral Meta Monogenic Solutions 354
20.4.1 The Propagating Kernel 354
20.4.2 Green Function 356
20.4.3 Path Integral Formulation (PIF) 357
20.5 Summary 358
21 Mobius Transformations, Vahlen Matrices, and
their Factorization
Pertti Lounesto 361
21.1 Similarities and transversions 361
21.2 The counter example of J. Maks 362
21.3 Recent mistakes in factorization 363
21.4 How to factor Vahlen matrices? 364
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| id | DE-604.BV010769702 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:58:34Z |
| institution | BVB |
| isbn | 0849384818 |
| language | English |
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| physical | VII, 366 Seiten Ill., graph. Darst. |
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| spelling | Clifford algebras in analysis and related topics John Ryan, University of Arkansas Boca Raton, Fla. [u.a.] CRC Press 1996 VII, 366 Seiten Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in Advanced Mathematics Clifford-Algebra (DE-588)4199958-7 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content (DE-588)1071861417 Konferenzschrift gnd-content Clifford-Algebra (DE-588)4199958-7 s DE-604 Ryan, John 1955- Sonstige (DE-588)1037810732 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007192111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Clifford algebras in analysis and related topics Clifford-Algebra (DE-588)4199958-7 gnd |
| subject_GND | (DE-588)4199958-7 (DE-588)4143413-4 (DE-588)1071861417 |
| title | Clifford algebras in analysis and related topics |
| title_auth | Clifford algebras in analysis and related topics |
| title_exact_search | Clifford algebras in analysis and related topics |
| title_full | Clifford algebras in analysis and related topics John Ryan, University of Arkansas |
| title_fullStr | Clifford algebras in analysis and related topics John Ryan, University of Arkansas |
| title_full_unstemmed | Clifford algebras in analysis and related topics John Ryan, University of Arkansas |
| title_short | Clifford algebras in analysis and related topics |
| title_sort | clifford algebras in analysis and related topics |
| topic | Clifford-Algebra (DE-588)4199958-7 gnd |
| topic_facet | Clifford-Algebra Aufsatzsammlung Konferenzschrift |
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