Functional analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin, [u.a.]
Springer
[1995]
|
| Edition: | Reprint of the 1980 edition, 6. edition |
| Series: | Classics in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Originally published as Vol. 123 of the Grundlehren der mathematischen Wissenschaften |
| Physical Description: | XII, 500 Seiten Illustrationen |
| ISBN: | 3540586547 |
Staff View
MARC
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| 100 | 1 | |a Yoshida, Kōsaku |d 1909-1990 |0 (DE-588)119082519 |4 aut | |
| 245 | 1 | 0 | |a Functional analysis |c Kôsaku Yosida |
| 250 | |a Reprint of the 1980 edition, 6. edition | ||
| 264 | 1 | |a Berlin, [u.a.] |b Springer |c [1995] | |
| 264 | 4 | |c © 1995 | |
| 300 | |a XII, 500 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Classics in mathematics | |
| 500 | |a Originally published as Vol. 123 of the Grundlehren der mathematischen Wissenschaften | ||
| 650 | 4 | |a Functional analysis | |
| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Funktionalanalysis |0 (DE-588)4018916-8 |D s |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009212889 | |
Record in the Search Index
| _version_ | 1828828203998773248 |
|---|---|
| adam_text |
Contents
0.
Preliminaries
.1
1.
Set Theory
. 1
2.
Topological Spaces
. 3
3.
Measure Spaces
. 16
4.
Linear Spaces
. 20
1. Semi-norms
. 23
1.
Semi-norms and Locally Convex Linear Topological Spaces
. 23
2.
Norms and Quasi-norms
. 30
3.
Examples of Normed Linear Spaces
. 32
4.
Examples of Quasi-normed Linear Spaces
. 38
5.
Pre-Hilbert Spaces
. 39
6.
Continuity of Linear Operators
. 42
7.
Bounded Sets and Bornologic Spaces
. 44
8.
Generalized Functions and Generalized Derivatives
. 46
9.
B-spaces and .F-spaces
. 52
10.
The Completion
. 66
11.
Factor Spaces of a B-space
. 69
12.
The Partition of Unity
. 60
13.
Generalized Functions with Compact Support
. 62
14.
The Direct Product of Generalized Functions
. 66
II. Applications of the Baire-Hausdorff Theorem
. 68
1.
The Uniform Boundedness Theorem and the Resonance
Theorem
. 68
2.
The Vitali-Hahn-Saks Theorem
. 70
3.
The Termwise Differentiability of a Sequence of Generalized
Functions
. 72
4.
The Principle of the Condensation of Singularities
. 72
6.
The Open Mapping Theorem
.·. 75
6.
The Closed Graph Theorem
. 77
7.
An Application of the Closed Graph Theorem
(Hörmander's
Theorem)
. 80
III. The Orthogonal Projection and F. Riesz' Representation Theo¬
rem
. 81
1.
The Orthogonal Projection
. 81
2.
"Nearly Orthogonal" Elements
. 84
Contents
IX
3. The
Ascoli-Arzelà
Theorem
.85
4.
The Orthogonal Base. Bessel's Inequality and
Parsevaľs
Relation
.86
6.
E. Schmidt's Orthogonalization
. 88
6.
F. Riesz' Representation Theorem
. 90
7.
The Lax-Milgram Theorem
. 92
8.
A Proof of the Lebesgue-Nikodym Theorem
. 93
9.
The Aronszajn-Bergman Reproducing Kernel
. 96
10.
The Negative Norm of P. Lax
.98
11.
Local Structures of Generalized Functions
.100
IV. The Hahn-Banach Theorems
.102
1.
The Hahn-Banach Extension Theorem in Real Linear Spaces
102
2.
The Generalized Limit
.103
3.
Locally Convex, Complete Linear Topological Spaces
. . . 104
4.
The Hahn-Banach Extension Theorem in Complex Linear
Spaces
.105
6.
The Hahn-Banach Extension Theorem in Normed Linear
Spaces
.106
6.
The Existence of Non-trivial Continuous Linear Functional
107
7.
Topologies of Linear Maps
. . .110
8.
The Embedding of X in its Bidual Space X"
.112
9.
Examples of Dual Spaces
.114
V. Strong Convergence and Weak Convergence
.119
1.
The Weak Convergence and The Weak* Convergence
. . . 120
2.
The Local Sequential Weak Compactness of Reflexive B-
spaces. The Uniform Convexity
.126
3.
Dunford's Theorem and The Gelfand-Mazur Theorem
. 128
4.
The Weak and Strong Measurability. Pettis' Theorem
. 130
5.
Bochner's Integral
.132
Appendix to Chapter V. Weak Topologies and Duality in Locally
Convex Linear Topological Spaces
.136
1.
Polar Sets
. 136
2.
Barrel Spaces
. 138
3.
Semi-reflexivity and
Reflexivity
. 139
4.
The Eberlein-Shmulyan Theorem
. 141
VI. Fourier Transform and Differential Equations
.146
1.
The Fourier Transform of Rapidly Decreasing Functions
. 146
2.
The Fourier Transform of Tempered Distributions
.149
3.
Convolutions
.166
4.
The Paley-Wiener Theorems. The One-sided Laplace Trans¬
form
.161
6.
Titchmarsh's Theorem
.166
6.
Mikusinski's Operational Calculus
.169
7.
Sobolev's Lemma
.173
X
Contents
8.
Girdmg's Inequality
.176
9. Friedrichs'
Theorem
.177
10.
The Malgrange-Ehrenpreis Theorem
.182
11.
Differential Operators with Uniform Strength
.188
12.
The Hypoellipticity
(Hörmander's
Theorem)
.189
VII.
Dual Operators
.193
1.
Dual Operators
. 193
2.
Adjoint Operators
. 196
3.
Symmetric Operators and Self-adjoint Operators
. 197
4.
Unitary Operators. The Cayley Transform
. 202
6.
The Closed Range Theorem
. 206
VIII.
Resolvent and Spectrum
.209
1.
The Resolvent and Spectrum
. 209
2.
The Resolvent Equation and Spectral Radius
. 211
3.
The Mean Ergodic Theorem
. 213
4.
Ergodic Theorems of the Hille Type Concerning Pseudo-
resolvents
. 216
6.
The Mean Value of an Almost Periodic Function
. 218
6.
The Resolvent of a Dual Operator
. 224
7.
Dunford's Integral
. 225
8.
The Isolated Singularities of a Resolvent
. 228
IX. Analytical Theory of Semi-groups
.231
1.
The Semi-group of Class (Cj)
.232
2.
The Equi-continuous Semi-group of Class (Co) in Locally
Convex Spaces. Examples of Semi-groups
.234
3.
The Infinitesimal Generator of an Equi-continuous Semi¬
group of Class (Cj)
.237
4.
The Resolvent of the Infinitesimal Generator A
.240
5.
Examples of Infinitesimal Generators
.242
6.
The Exponential of a Continuous Linear Operator whose
Powers are Equi-continuous
.244
7.
The Representation and the Characterization of Equi-con¬
tinuous Semi-groups of Class
(Co)
in Terms of the Corre¬
sponding Infinitesimal Generators
.246
8.
Contraction Semi-groups and Dissipative Operators
. 250
9.
Equi-continuous Groups of Class (C,,). Stone's Theorem
. . 251
10.
Holomorphic Semi-groups
. 254
11.
Fractional Powers of Closed Operators
. 259
12.
The Convergence of Semi-groups. The Trotter-Kato Theorem
269
13.
Dual Semi-groups. Phillips' Theorem
. 272
X. Compact Operators
.274
1.
Compact Sets in ¿-spaces
.274
2.
Compact Operators and Nuclear Operators
.277
Contents
XI
3. The
Rellich-Gàrding
Theorem
. 281
4.
Schauder's Theorem
. 282
5.
The Riesz-Schauder Theory
. 283
6.
Dirichlet's Problem
.
28fi
Appendix to Chapter X. The Nuclear Space of A. Grothendieck
28!)
XI. Normed Rings and Spectral Representation
.294
1.
Maximal Ideals of a Normed Ring
.295
2.
The Radical. The Semi-simplicity
.298
3.
The Spectral Resolution of Bounded Normal Operators
. . 302
4.
The Spectral Resolution of a Unitary Operator
.306
6.
The Resolution of the Identity
.309
6.
The Spectral Resolution of a Self-adjoint Operator
. 313
7.
Real Operators and Semi-bounded Operators.
Friedrichs'
Theorem
.31«
8.
The Spectrum of a Self-adjoint Operator. Rayleigh's Prin¬
ciple and the Krylov-Weinstein Theorem. The Multiplicity
of the Spectrum
.319
9.
The General Expansion Theorem. A Condition for the
Absence of the Continuous Spectrum
.323
10.
The Peter-Weyl-Neumann Theorem
. 326
11.
Tannaka's Duality Theorem for Non-commutative Compact
Groups
. 332
12.
Functions of a Self-adjoint Operator
. 338
13.
Stone's Theorem and Bochner's Theorem
. 345
14.
A Canonical Form of a Self-adjoint Operator with Simple
Spectrum
. 347
15.
The Defect Indices of a Symmetric Operator. The Generalized
Resolution of the Identity
. 349
16.
The Group-ring
Ľ
and Wiener's Tauberian Theorem
. . . 354
XII.
Other Representation Theorems in Linear Spaces
.362
1.
Extremal Points. The Krein-Milman Theorem
. 362
2.
Vector Lattices
. 364
3.
B-lattices and .F-lattices
. 369
4.
A Convergence Theorem of Banach
. 370
5.
The Representation of a Vector Lattice as Point Functions
372
6.
The Representation of a Vector Lattice as Set Functions
. 375
XIII.
Ergodic Theory and Diffusion Theory
.379
1.
The Markov Process with an Invariant Measure
.379
2.
An Individual Ergodic Theorem and Its Applications
. . . 383
3.
The Ergodic Hypothesis and the H-theorem
.389
4.
The Ergodic Decomposition of a Markov Process with a
Locally Compact Phase Space
.393
5.
The Brownian Motion on a Homogeneous Riemannian Space
398
6.
The Generalized Laplacian of W. Feller
.403
7.
An Extension of the Diffusion Operator
.408
8.
Markov Processes and Potentials
.410
9.
Abstract Potential Operators and Semi-groups
.411
XII Contents
XIV.
The Integration of the Equation of Evolution
.418
1.
Integration of Diffusion Equations in L* (R1*)
. 419
2.
Integration of Diffusion Equations in a Compact Rie-
mannian Space
. 425
3.
Integration of Wave Equations in a Euclidean Space Rm
427
4.
Integration of Temporally Inhomogeneous Equations of
Evolution in a B-space
. 430
6.
The Method of Tanabe and Soboi.evski
.438
6.
Non-linear Evolution Equations
1
(The
Kõmura-Kato
Approach)
.445
7.
Non-linear Evolution Equations
2
(The Approach through
the Crandall-Liggett Convergence Theorem)
.454
Supplementary Notes
.466
Bibliography
. . 469
Index
.487
Notation of Spaces
.501 |
| any_adam_object | 1 |
| author | Yoshida, Kōsaku 1909-1990 |
| author_GND | (DE-588)119082519 |
| author_facet | Yoshida, Kōsaku 1909-1990 |
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| author_sort | Yoshida, Kōsaku 1909-1990 |
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| classification_tum | MAT 460f |
| ctrlnum | (OCoLC)31374639 (DE-599)BVBBV013497150 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-search | 515.7 |
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| discipline | Mathematik |
| edition | Reprint of the 1980 edition, 6. edition |
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| id | DE-604.BV013497150 |
| illustrated | Illustrated |
| indexdate | 2025-04-08T10:01:26Z |
| institution | BVB |
| isbn | 3540586547 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009212889 |
| oclc_num | 31374639 |
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| owner_facet | DE-19 DE-BY-UBM DE-703 DE-355 DE-BY-UBR DE-739 DE-92 DE-1046 DE-91G DE-BY-TUM DE-11 DE-83 |
| physical | XII, 500 Seiten Illustrationen |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | Springer |
| record_format | marc |
| series2 | Classics in mathematics |
| spelling | Yoshida, Kōsaku 1909-1990 (DE-588)119082519 aut Functional analysis Kôsaku Yosida Reprint of the 1980 edition, 6. edition Berlin, [u.a.] Springer [1995] © 1995 XII, 500 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Classics in mathematics Originally published as Vol. 123 of the Grundlehren der mathematischen Wissenschaften Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Funktionalanalysis (DE-588)4018916-8 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-61859-8 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009212889&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yoshida, Kōsaku 1909-1990 Functional analysis Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4123623-3 |
| title | Functional analysis |
| title_auth | Functional analysis |
| title_exact_search | Functional analysis |
| title_full | Functional analysis Kôsaku Yosida |
| title_fullStr | Functional analysis Kôsaku Yosida |
| title_full_unstemmed | Functional analysis Kôsaku Yosida |
| title_short | Functional analysis |
| title_sort | functional analysis |
| topic | Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Funktionalanalysis Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009212889&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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