Pseudo-differential operators and symmetries: background analysis and advanced topics
Gespeichert in:
Beteiligte Personen: | , |
---|---|
Format: | Buch |
Sprache: | Englisch |
Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2010
|
Schriftenreihe: | Pseudo-differential operators
2 |
Schlagwörter: | |
Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017321516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
Umfang: | XIV, 709 S. 235 mm x 165 mm |
ISBN: | 9783764385132 |
Internformat
MARC
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100 | 1 | |a Ruzhansky, Michael |d 1972- |e Verfasser |0 (DE-588)139579605 |4 aut | |
245 | 1 | 0 | |a Pseudo-differential operators and symmetries |b background analysis and advanced topics |c Michael Ruzhansky ; Ville Turunen |
264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2010 | |
300 | |a XIV, 709 S. |c 235 mm x 165 mm | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a Pseudo-differential operators |v 2 | |
650 | 4 | |a Pseudodifferential operators | |
650 | 0 | 7 | |a Pseudodifferentialoperator |0 (DE-588)4047640-6 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Symmetrischer Raum |0 (DE-588)4184206-6 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Kompakte Lie-Gruppe |0 (DE-588)4164846-8 |2 gnd |9 rswk-swf |
689 | 0 | 0 | |a Pseudodifferentialoperator |0 (DE-588)4047640-6 |D s |
689 | 0 | 1 | |a Symmetrischer Raum |0 (DE-588)4184206-6 |D s |
689 | 0 | |5 DE-604 | |
689 | 1 | 0 | |a Pseudodifferentialoperator |0 (DE-588)4047640-6 |D s |
689 | 1 | 1 | |a Kompakte Lie-Gruppe |0 (DE-588)4164846-8 |D s |
689 | 1 | |5 DE-604 | |
700 | 1 | |a Turunen, Ville |e Verfasser |0 (DE-588)139579877 |4 aut | |
776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-7643-8514-9 |
830 | 0 | |a Pseudo-differential operators |v 2 |w (DE-604)BV035815877 |9 2 | |
856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017321516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-017321516 |
Datensatz im Suchindex
DE-BY-TUM_call_number | 0102 MAT 474f 2009 A 9219 |
---|---|
DE-BY-TUM_katkey | 1682582 |
DE-BY-TUM_location | 01 |
DE-BY-TUM_media_number | 040010220981 |
_version_ | 1821933640099037185 |
adam_text | CONTENTS PREFACE XIII INTRODUCTION 1 PART I FOUNDATIONS OF ANALYSIS A
SETS, TOPOLOGY AND METRICS A.I SETS, COLLECTIONS, FAMILIES 9 A.2
RELATIONS, FUNCTIONS, EQUIVALENCES AND ORDERS 12 A.3 DOMINOES TUMBLING
AND TRANSFINITE INDUCTION 16 A.4 AXIOM OF CHOICE: EQUIVALENT
FORMULATIONS 17 A.5 WELL-ORDERING PRINCIPLE REVISITED 25 A.6 METRIC
SPACES 26 A.7 TOPOLOGICAL SPACES 29 A.8 KURATOWSKI S CLOSURE 35 A.9
COMPLETE METRIC SPACES 40 A. 10 CONTINUITY AND HOMEOMORPHISMS 46 A. 11
COMPACT TOPOLOGICAL SPACES 49 A.12 COMPACT HAUSDORFF SPACES 52 A. 13
SEQUENTIAL COMPACTNESS 57 A.14 STONE-WEIERSTRASS THEOREM 62 A.15
MANIFOLDS 65 A. 16 CONNECTEDNESS AND PATH-CONNECTEDNESS 66 A.17
CO-INDUCTION AND QUOTIENT SPACES 69 A.18 INDUCTION AND PRODUCT SPACES 70
A.19 METRISABLE TOPOLOGIES 74 A.20 TOPOLOGY VIA GENERALISED SEQUENCES 77
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/99213630X DIGITALISIERT
DURCH VI CONTENTS B ELEMENTARY FUNCTIONAL ANALYSIS B.I VECTOR SPACES 79
B.I.I TENSOR PRODUCTS 83 B.2 TOPOLOGICAL VECTOR SPACES 85 B.3 LOCALLY
CONVEX SPACES 87 B.3.1 TOPOLOGICAL TENSOR PRODUCTS 90 B.4 BANACH SPACES
92 B.4.1 BANACH SPACE ADJOINT 101 B.5 HUBERT SPACES 103 B.5.1 TRACE
CLASS, HILBERT-SCHMIDT, AND SCHATTEN CLASSES . . . . ILL C MEASURE
THEORY AND INTEGRATION C.I MEASURES AND OUTER MEASURES 116 C.I.I
MEASURING SETS 116 C.I.2 BOREI REGULARITY 124 C.1.3 ON LEBESGUE MEASURE
128 C.I.4 LEBESGUE NON-MEASURABLE SETS 133 C.2 MEASURABLE FUNCTIONS 134
C.2.1 WELL-BEHAVING FUNCTIONS 134 C.2.2 SEQUENCES OF MEASURABLE
FUNCTIONS 137 C.2.3 APPROXIMATING MEASURABLE FUNCTIONS 141 C.3
INTEGRATION 143 C.3.1 INTEGRATING SIMPLE NON-NEGATIVE FUNCTIONS 144
C.3.2 INTEGRATING NON-NEGATIVE FUNCTIONS 144 C.3.3 INTEGRATION IN
GENERAL 147 C.4 INTEGRAL AS A FUNCTIONAL 152 C.4.1 LEBESGUE SPACES L P
(SS) 152 C.4.2 SIGNED MEASURES 158 C.4.3 DERIVATIVES OF SIGNED MEASURES
162 C.4.4 INTEGRATION AS FUNCTIONAL ON FUNCTION SPACES 169 C.4.5
INTEGRATION AS FUNCTIONAL ON L P ((I) 170 C.4.6 INTEGRATION AS
FUNCTIONAL ON C(X) CONTENTS VII PART II COMMUTATIVE SYMMETRIES 1 FOURIER
ANALYSIS ON R 1.1 BASIC PROPERTIES OF THE FOURIER TRANSFORM 221 1.2
USEFUL INEQUALITIES 229 1.3 TEMPERED DISTRIBUTIONS 233 1.3.1 FOURIER
TRANSFORM OF TEMPERED DISTRIBUTIONS 233 1.3.2 OPERATIONS WITH
DISTRIBUTIONS 236 1.3.3 APPROXIMATING BY SMOOTH FUNCTIONS 239 1.4
DISTRIBUTIONS 241 1.4.1 LOCALISATION OF //-SPACES AND DISTRIBUTIONS 241
1.4.2 CONVOLUTION OF DISTRIBUTIONS 244 1.5 SOBOLEV SPACES 246 1.5.1 WEAK
DERIVATIVES AND SOBOLEV SPACES 246 1.5.2 SOME PROPERTIES OF SOBOLEV
SPACES 249 1.5.3 MOLLIFIERS 250 1.5.4 APPROXIMATION OF SOBOLEV SPACE
FUNCTIONS 253 1.6 INTERPOLATION 255 2 PSEUDO-DIFFERENTIAL OPERATORS ON W
1 2.1 MOTIVATION AND DEFINITION 259 2.2 AMPLITUDE REPRESENTATION OF
PSEUDO-DIFFERENTIAL OPERATORS .... 263 2.3 KERNEL REPRESENTATION OF
PSEUDO-DIFFERENTIAL OPERATORS 264 2.4 BOUNDEDNESS ON L 2 (R N ) 267 2.5
CALCULUS OF PSEUDO-DIFFERENTIAL OPERATORS 271 2.5.1 COMPOSITION FORMULAE
271 2.5.2 CHANGES OF VARIABLES 281 2.5.3 PRINCIPAL SYMBOL AND CLASSICAL
SYMBOLS 282 2.5.4 CALCULUS PROOF OF L 2 -BOUNDEDNESS 284 2.5.5
ASYMPTOTIC SUMS 285 2.6 APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS
287 2.6. CONTENTS 3.3.4 LINKING DIFFERENCES TO DERIVATIVES 321 3.4
PERIODIC TAYLOR EXPANSION 327 3.5 APPENDIX: ON OPERATORS IN BANACH
SPACES 329 PSEUDO-DIFFERENTIAL OPERATORS ON T* 4.1 TOROIDAL SYMBOLS 335
4.1.1 QUANTIZATION OF OPERATORS ON T* 335 4.1.2 TOROIDAL SYMBOLS 337
4.1.3 TOROIDAL AMPLITUDES 340 4.2 PSEUDO-DIFFERENTIAL OPERATORS ON
SOBOLEV SPACES 342 4.3 KERNELS OF PERIODIC PSEUDO-DIFFERENTIAL OPERATORS
347 4.4 ASYMPTOTIC SUMS AND AMPLITUDE OPERATORS 351 4.5 EXTENSION OF
TOROIDAL SYMBOLS 356 4.6 PERIODISATION OF PSEUDO-DIFFERENTIAL OPERATORS
360 4.7 SYMBOLIC CALCULUS 367 4.8 OPERATORS ON L 2 (T ) AND SOBOLEV
SPACES 374 4.9 ELLIPTIC PSEUDO-DIFFERENTIAL OPERATORS ON T* 376 4.10
SMOOTHNESS PROPERTIES 382 4.11 AN APPLICATION TO PERIODIC INTEGRAL
OPERATORS 387 4.12 TOROIDAL WAVE FRONT SETS 389 4.13 FOURIER SERIES
OPERATORS 393 4.14 BOUNDEDNESS OF FOURIER SERIES OPERATORS ON L 2 (T N )
405 4.15 AN APPLICATION TO HYPERBOLIC EQUATIONS 410 COMMUTATOR
CHARACTERISATION OF PSEUDO-DIFFERENTIAL OPERATORS 5.1 EUCLIDEAN
COMMUTATOR CHARACTERISATION 413 5.2 PSEUDO-DIFFERENTIAL OPERATORS ON
MANIFOLDS 416 5.3 COMMUTATOR CHARACTERISATION ON CLOSED MANIFOLDS 421
5.4 TOROIDAL COMMUTATOR CHARACTERISATION 423 PART III REPRESENTATION
THEORY OF COMPACT GROUPS 6 CONTENTS IX 7.4 HAAR MEASURE AND INTEGRAL 453
7.4.1 INTEGRATION ON QUOTIENT SPACES 462 7.5 PETER-WEYL DECOMPOSITION OF
REPRESENTATIONS 465 7.6 FOURIER SERIES AND TRIGONOMETRIC POLYNOMIALS 474
7.7 CONVOLUTIONS 478 7.8 CHARACTERS 479 7.9 INDUCED REPRESENTATIONS 482
8 LINEAR LIE GROUPS 8.1 EXPONENTIAL MAP 492 8.2 NO SMALL SUBGROUPS FOR
LIE, PLEASE 496 8.3 LIE GROUPS AND LIE ALGEBRAS 498 8.3.1 UNIVERSAL
ENVELOPING ALGEBRA 506 8.3.2 CASIMIR ELEMENT AND LAPLACE OPERATOR 510 9
HOPF ALGEBRAS 9.1 COMMUTATIVE C*-ALGEBRAS 515 9.2 HOPF ALGEBRAS 517 PART
IV NON-COMMUTATIVE SYMMETRIES 10 PSEUDO-DIFFERENTIAL OPERATORS ON
COMPACT LIE GROUPS 10.1 INTRODUCTION 529 10.2 FOURIER SERIES ON COMPACT
LIE GROUPS 530 10.3 FUNCTION SPACES ON THE UNITARY DUAL 534 10.3.1
SPACES ON THE GROUP G 534 10.3.2 SPACES ON THE DUAL G 536 10.3.3 SPACES
L P (G) 546 10.4 SYMBOLS OF OPERATORS 550 10.4.1 FULL SYMBOLS 552 10.4.2
CONJUGATION PROPERTIES OF SYMBOLS 556 10.5 BOUNDEDNESS OF OPERATORS ON L
2 {G) 559 10.6 TAYLOR EXPANSION ON LIE GROUPS 561 10.7 SYMBOLIC CALCULUS
563 10.7. X CONTENTS 10.9.2 SYMBOL CLASSES E M (G) 575 10.10 FULL
SYMBOLS ON COMPACT MANIFOLDS 578 10.11 OPERATOR-VALUED SYMBOLS 579
10.11.1 EXAMPLE ON THE TORUS T * 589 10.12 APPENDIX: INTEGRAL KERNELS
591 11 FOURIER ANALYSIS ON SU(2) 11.1 PRELIMINARIES: GROUPS U(L), SO(2),
AND SO(3) 595 11.1.1 EULER ANGLES ON SO(3) 597 11.1.2 PARTIAL
DERIVATIVES ON SO(3) 598 11.1.3 INVARIANT INTEGRATION ON SO (3) 598 11.2
GENERAL PROPERTIES OF SU(2) 599 11.3 EULER ANGLE PARAMETRISATION OF
SU(2) 600 11.4 QUATERNIONS 603 11.4.1 QUATERNIONS AND SU(2) 603 11.4.2
QUATERNIONS AND SO(3) 604 11.4.3 INVARIANT INTEGRATION ON SU(2) 605
11.4.4 SYMPLECTIC GROUPS 605 11.5 LIE ALGEBRA AND DIFFERENTIAL OPERATORS
ON SU(2) 607 11.6 IRREDUCIBLE UNITARY REPRESENTATIONS OF SU(2) 612
11.6.1 REPRESENTATIONS OF SO(3) 615 11.7 MATRIX ELEMENTS OF
REPRESENTATIONS OF SU(2) 616 11.8 MULTIPLICATION FORMULAE FOR
REPRESENTATIONS OF SU(2) 620 11.9 LAPLACIAN AND DERIVATIVES OF
REPRESENTATIONS ON SU(2) 624 11.10 FOURIER SERIES ON SU(2) AND ON SO(3)
629 12 PSEUDO-DIFFERENTIAL OPERATORS ON SU(2) 12.1 SYMBOLS OF OPERATORS
ON SU(2) 631 12.2 SYMBOLS OF D + ,D-,D 0 AND LAPLACIAN C 634 12.3
DIFFERENCE OPERATORS FOR SYMBOLS 636 12.3. CONTENTS XI 13
PSEUDO-DIFFERENTIAL OPERATORS ON HOMOGENEOUS SPACES 13.1 ANALYSIS ON
CLOSED MANIFOLDS 667 13.2 ANALYSIS ON COMPACT HOMOGENEOUS SPACES 669
13.3 ANALYSIS ON K G, K A TORUS 673 13.4 LIFTING OF OPERATORS 679
BIBLIOGRAPHY 683 NOTATION 693 INDEX 697
|
any_adam_object | 1 |
author | Ruzhansky, Michael 1972- Turunen, Ville |
author_GND | (DE-588)139579605 (DE-588)139579877 |
author_facet | Ruzhansky, Michael 1972- Turunen, Ville |
author_role | aut aut |
author_sort | Ruzhansky, Michael 1972- |
author_variant | m r mr v t vt |
building | Verbundindex |
bvnumber | BV035400869 |
callnumber-first | Q - Science |
callnumber-label | QA329 |
callnumber-raw | QA329.7 |
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classification_rvk | SK 620 |
classification_tum | MAT 587f MAT 225f MAT 474f |
ctrlnum | (OCoLC)310401037 (DE-599)DNB99213630X |
dewey-full | 515.7 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 515 - Analysis |
dewey-raw | 515.7 |
dewey-search | 515.7 |
dewey-sort | 3515.7 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Book |
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id | DE-604.BV035400869 |
illustrated | Not Illustrated |
indexdate | 2024-12-20T13:31:39Z |
institution | BVB |
isbn | 9783764385132 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017321516 |
oclc_num | 310401037 |
open_access_boolean | |
owner | DE-91G DE-BY-TUM DE-824 DE-19 DE-BY-UBM DE-11 DE-355 DE-BY-UBR |
owner_facet | DE-91G DE-BY-TUM DE-824 DE-19 DE-BY-UBM DE-11 DE-355 DE-BY-UBR |
physical | XIV, 709 S. 235 mm x 165 mm |
publishDate | 2010 |
publishDateSearch | 2010 |
publishDateSort | 2010 |
publisher | Birkhäuser |
record_format | marc |
series | Pseudo-differential operators |
series2 | Pseudo-differential operators |
spellingShingle | Ruzhansky, Michael 1972- Turunen, Ville Pseudo-differential operators and symmetries background analysis and advanced topics Pseudo-differential operators Pseudodifferential operators Pseudodifferentialoperator (DE-588)4047640-6 gnd Symmetrischer Raum (DE-588)4184206-6 gnd Kompakte Lie-Gruppe (DE-588)4164846-8 gnd |
subject_GND | (DE-588)4047640-6 (DE-588)4184206-6 (DE-588)4164846-8 |
title | Pseudo-differential operators and symmetries background analysis and advanced topics |
title_auth | Pseudo-differential operators and symmetries background analysis and advanced topics |
title_exact_search | Pseudo-differential operators and symmetries background analysis and advanced topics |
title_full | Pseudo-differential operators and symmetries background analysis and advanced topics Michael Ruzhansky ; Ville Turunen |
title_fullStr | Pseudo-differential operators and symmetries background analysis and advanced topics Michael Ruzhansky ; Ville Turunen |
title_full_unstemmed | Pseudo-differential operators and symmetries background analysis and advanced topics Michael Ruzhansky ; Ville Turunen |
title_short | Pseudo-differential operators and symmetries |
title_sort | pseudo differential operators and symmetries background analysis and advanced topics |
title_sub | background analysis and advanced topics |
topic | Pseudodifferential operators Pseudodifferentialoperator (DE-588)4047640-6 gnd Symmetrischer Raum (DE-588)4184206-6 gnd Kompakte Lie-Gruppe (DE-588)4164846-8 gnd |
topic_facet | Pseudodifferential operators Pseudodifferentialoperator Symmetrischer Raum Kompakte Lie-Gruppe |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017321516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV035815877 |
work_keys_str_mv | AT ruzhanskymichael pseudodifferentialoperatorsandsymmetriesbackgroundanalysisandadvancedtopics AT turunenville pseudodifferentialoperatorsandsymmetriesbackgroundanalysisandadvancedtopics |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
Signatur: |
0102 MAT 474f 2009 A 9219
Lageplan |
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Exemplar 1 | Ausleihbar Am Standort |