Time-frequency analysis of operators:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2020]
|
| Schriftenreihe: | De Gruyter studies in mathematics
volume 75 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032537986&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIV, 442 Seiten Diagramme |
| ISBN: | 9783110530353 311053035X |
Internformat
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| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Cordero, Elena |d 1973- |e Verfasser |0 (DE-588)1183842120 |4 aut | |
| 245 | 1 | 0 | |a Time-frequency analysis of operators |c Elena Cordero, Luigi Rodino |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2020] | |
| 264 | 4 | |c © 2020 | |
| 300 | |a XIV, 442 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematics |v volume 75 | |
| 653 | |a Fourier-Integraloperator | ||
| 653 | |a Gabor-Transformation | ||
| 653 | |a Nichtlineare Wellengleichung | ||
| 653 | |a Pseudodifferentialoperator | ||
| 653 | |a Zeit-Frequenz-Analyse | ||
| 700 | 1 | |a Rodino, Luigi |d 1948- |e Verfasser |0 (DE-588)1136343946 |4 aut | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-053245-6 |
| 830 | 0 | |a De Gruyter studies in mathematics |v volume 75 |w (DE-604)BV000005407 |9 75 | |
| 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=032537986&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-032537986 | |
Datensatz im Suchindex
| _version_ | 1819370392691671040 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
VII
INTRODUCTION
-----
IX
0
PRELIMINARIES
*
1
0.1
NOTATION
AND
BACKGROUND
*
1
0.2
FUNCTION
SPACES
AND
FOURIER
TRANSFORM
*
3
0.2.1
FUNDAMENTAL
OPERATORS
*
6
0.2.2
GAUSSIAN
FUNCTIONS
*
7
1
BASICS
OF
TIME-FREQUENCY
REPRESENTATIONS
AND
RELATED
PROPERTIES
-
*
9
1.1
HINTS
ON
SYMPLECTIC
AND
METAPLECTIC
GROUPS
*
12
1.1.1
THE
SYMPLECTIC
GROUP
*
12
1.1.2
THE
METAPLECTIC
GROUP
*
13
1.1.3
THE
SYMPLECTIC
FOURIER
TRANSFORM
*
17
1.2
TIME-FREQUENCY
REPRESENTATIONS
*
18
1.2.1
THE
SHORT-TIME
FOURIER
TRANSFORM
*
18
1.2.2
ORTHOGONALITY
RELATIONS
*
24
1.2.3
SHORT-TIME
FOURIER
TRANSFORM
AND
SYMPLECTIC
MATRICES
*
25
1.2.4
REPRODUCING
FORMULA
FOR
THE
SHORT-TIME
FOURIER
TRANSFORM
*
26
1.2.5
SHORT-TIME
FOURIER
TRANSFORM
OF
TEMPERED
DISTRIBUTIONS
*
28
1.2.6
DECAY
AND
FURTHER
PROPERTIES
*
36
1.3
AMBIGUITY
FUNCTION,
WIGNER
DISTRIBUTION,
AND
RELATED
TOPICS
*
38
1.3.1
THE
AMBIGUITY
FUNCTION
*
38
1.3.2
THE
WIGNER
DISTRIBUTION
*
39
1.3.3
MARGINAL
DENSITIES
*
44
1.3.4
THE
COHEN
CLASS
*
46
1.3.5
R-WIGNER
DISTRIBUTIONS
*
53
1.3.6
TIME-FREQUENCY
REPRESENTATIONS
OF
GAUSSIANS
*
60
1.3.7
SHORT-TIME
FOURIER
TRANSFORM
OF
TIME-FREQUENCY
REPRESENTATIONS
*
64
2
FUNCTION
SPACES
*
69
2.1
WEIGHT
FUNCTIONS
*
72
2.2
MIXED
NORM
SPACES
*
76
2.3
MODULATION
SPACES
*
79
2.3.1
PROPERTIES
OF
MODULATION
SPACES
*
81
2.3.2
ALTERNATIVE
DEFINITION
OF
MODULATION
SPACES
USING
FREQUENCY-UNIFORM
LOCALIZATION
TECHNIQUES
*
95
2.4
WIENER
AMALGAM
SPACES
*
100
XII
*
CONTENTS
2.4.1
INCLUSION,
CONVOLUTION,
AND
MULTIPLICATION
RELATIONS
*
107
2.5
DILATION
PROPERTIES
FOR
WIENER
AMALGAM
SPACES
W(L
P
,L
Q
)
*
113
2.6
DILATION
PROPERTIES
FOR
MODULATION
SPACES
*
118
2.7
SHARPNESS
OF
CONVOLUTION,
INCLUSION,
AND
MULTIPLICATION
RELATIONS
FOR
MODULATION
SPACES
*
135
2.7.1
TIME-FREQUENCY
TOOLS
*
138
2.7.2
FURTHER
EXTENSIONS
OF
MODULATION
SPACES
(QUASI-BANACH
SETTING)
*
140
3
GABOR
FRAMES
AND
LINEAR
OPERATORS
*
143
3.1
FRAMES
IN
HILBERT
SPACES
*
145
3.1.1
FRAME
EXPANSIONS
AND
FRAME
OPERATOR
*
153
3.2
GABOR
FRAMES
*
162
3.2.1
EXISTENCE
AND
DENSITY
OF
GABOR
FRAMES
*
166
3.2.2
GABOR
FRAMES
FOR
MODULATION
SPACES
-----
176
3.3
KERNEL
THEOREMS
FOR
MODULATION
SPACES
*
181
3.3.1
OPERATORS
ACTING
ON
M
P,Q
*
187
4
PSEUDODIFFERENTIAL
OPERATORS
*
191
4.1
BOUNDEDNESS
ON
L
P
AND
WIENER
AMALGAM
SPACES
*
197
4.1.1
BOUNDEDNESS
ON
WIENER
AMALGAM
SPACES:
NECESSARY
CONDITIONS
*
201
4.2
SYMBOLS
IN
WIENER
AMALGAM
SPACES
*
208
4.3
PSEUDODIFFERENTIAL
OPERATORS
ON
MODULATION
SPACES
*
211
4.4
CONTINUITY
RESULTS
FOR
THE
(CROSS-)WIGNER
DISTRIBUTION
*
214
4.4.1
CONTINUITY
RESULTS
FOR
THE
SHORT-TIME
FOURIER
TRANSFORM
AND
THE
AMBIGUITY
FUNCTION
-----
223
4.4.2
PSEUDODIFFERENTIAL
OPERATORS
ON
MODULATION
SPACES,
CONCLUSIONS
*
226
4.4.3
LOCALIZATION
OPERATORS
ON
MODULATION
SPACES
*
227
4.5
OP
R
(A)
OPERATORS
WITH
SYMBOLS
IN
WIENER
AMALGAM
SPACES
*
230
4.5.1
BOUNDEDNESS
PROPERTIES
OF
R-WIGNER
DISTRIBUTIONS
*
232
4.5.2
CONTINUITY
PROPERTIES
OF
OP
T
(A)
OPERATORS
*
239
4.6
BORN-JORDAN
QUANTIZATION
AND
RELATED
PSEUDODIFFERENTIAL
CALCULUS
*
242
4.6.1
DIVISION
OF
DISTRIBUTIONS
*
245
4.6.2
CHANGES
OF
COORDINATES
FOR
TEMPERATE
DISTRIBUTIONS
*
250
4.6.3
BORN-JORDAN
PSEUDODIFFERENTIAL
OPERATORS
*
251
4.6.4
INVERTIBILITY
OF
THE
BORN-JORDAN
QUANTIZATION
*
253
4.7
BORN-JORDAN
PSEUDODIFFERENTIAL
OPERATORS
ON
MODULATION
SPACES
*
261
4.7.1
ANALYSIS
OF
THE
COHEN
KERNEL
0
*
263
4.7.2
PROOF
OF
THEOREM
4.7.1
-----
268
CONTENTS
*
XIII
5
TIME-FREQUENCY
ANALYSIS
OF
CONSTANT-COEFFICIENT
PARTIAL
DIFFERENTIAL
EQUATIONS
*
277
5.1
STRICHARTZ
ESTIMATES
FOR
THE
SCHRODINGER
EQUATION
IN
WIENER
AMALGAM
SPACES
*
281
5.1.1
5.1.2
5.1.3
5.2
5.2.1
5.2.2
5.2.3
5.2.4
FIXED-TIME
ESTIMATES
*
283
STRICHARTZ
ESTIMATES
*
287
SHARPNESS
OF
FIXED-TIME
AND
STRICHARTZ
ESTIMATES
*
295
GABOR
REPRESENTATIONS
OF
EVOLUTION
OPERATORS
*
301
GELFAND-SHILOV
SPACES
*
301
ALMOST
DIAGONALIZATION
FOR
PSEUDODIFFERENTIAL
OPERATORS
*
308
SPARSITY
OF
THE
GABOR
MATRIX
*
313
BOUNDEDNESS
OF
PSEUDODIFFERENTIAL
OPERATORS
ON
MODULATION
AND
GELFAND-SHILOV
SPACES
*
314
5.2.5
5.2.6
EVOLUTION
EQUATIONS
*
315
SOME
NUMERICS
FOR
THE
HEAT
EQUATION
*
321
6
FOURIER
INTEGRAL
OPERATORS
AND
APPLICATIONS
TO
SCHRODINGER
EQUATIONS
*
325
6.1
6.1.1
6.1.2
6.1.3
6.1.4
6.1.5
6.1.6
6.2
6.2.1
6.2.2
6.2.3
6.3
6.3.1
6.4
6.5
6.6
6.6.1
6.6.2
6.6.3
6.6.4
FOURIER
INTEGRAL
OPERATORS
*
326
PHASE
FUNCTIONS
AND
CANONICAL
TRANSFORMATIONS
*
328
ALMOST
DIAGONALIZATION
OF
FIOS
*
329
CONTINUITY
OF
FIOS
ON
M^(R
D
)
*
333
CONTINUITY
OF
FIOS
ON
M
P
*Q
*
336
MODULATION
SPACES
AS
SYMBOL
CLASSES
*
338
THE
CASE
OF
QUADRATIC
PHASES:
METAPLECTIC
OPERATORS
*
342
SPARSITY
OF
GABOR
REPRESENTATION
OF
SCHRODINGER
PROPAGATORS
*
349
CONTINUITY
OF
FIOS
ON
AF(LR
D
),
0
P
1
-----
351
SPARSITY
OF
THE
GABOR
MATRIX
AND
NONLINEAR
APPROXIMATION
*
352
APPLICATION
TO
THE
SOLUTION
OF
THE
SCHRODINGER
EQUATION
*
356
WIENER
ALGEBRAS
OF
FOURIER
INTEGRAL
OPERATORS
*
363
WIENER
ALGEBRA
PROPERTIES
*
367
FIOS
OF
TYPE
1
*
371
GENERALIZED
METAPLECTIC
OPERATORS
*
380
PROPAGATION
OF
GABOR
WAVE
FRONT
SET
FOR
SCHRODINGER
EQUATIONS
*
383
PRELIMINARIES
AND
SHUBIN
CLASSES
*
386
UNPERTURBED
SCHRODINGER
EQUATIONS
*
393
SCHRODINGER
EQUATIONS
WITH
BOUNDED
PERTURBATIONS
*
397
PROPAGATION
OF
SINGULARITIES
*
400
A
A.L
A.1.1
APPENDIX
-----
409
BASIS
THEORY
AND
SERIES EXPANSIONS
*
412
BASES
AND
ORTHONORMAL
SEQUENCES
*
412
XIV
*
CONTENTS
A.1.2
A.
2
CONVERGENCE
OF
SERIES
*
414
SOME
RESULTS
CONCERNING
REAL
INTERPOLATION
THEORY
*
421
BIBLIOGRAPHY
-----
425
INDEX
*
439
INDEX
OF
NOTATION
-----
441
|
| any_adam_object | 1 |
| author | Cordero, Elena 1973- Rodino, Luigi 1948- |
| author_GND | (DE-588)1183842120 (DE-588)1136343946 |
| author_facet | Cordero, Elena 1973- Rodino, Luigi 1948- |
| author_role | aut aut |
| author_sort | Cordero, Elena 1973- |
| author_variant | e c ec l r lr |
| building | Verbundindex |
| bvnumber | BV047131897 |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)1235993396 (DE-599)DNB1201236010 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV047131897 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T19:10:34Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110530353 311053035X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032537986 |
| oclc_num | 1235993396 |
| open_access_boolean | |
| owner | DE-29T DE-703 DE-11 |
| owner_facet | DE-29T DE-703 DE-11 |
| physical | XIV, 442 Seiten Diagramme |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spellingShingle | Cordero, Elena 1973- Rodino, Luigi 1948- Time-frequency analysis of operators De Gruyter studies in mathematics |
| title | Time-frequency analysis of operators |
| title_auth | Time-frequency analysis of operators |
| title_exact_search | Time-frequency analysis of operators |
| title_full | Time-frequency analysis of operators Elena Cordero, Luigi Rodino |
| title_fullStr | Time-frequency analysis of operators Elena Cordero, Luigi Rodino |
| title_full_unstemmed | Time-frequency analysis of operators Elena Cordero, Luigi Rodino |
| title_short | Time-frequency analysis of operators |
| title_sort | time frequency analysis of operators |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032537986&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT corderoelena timefrequencyanalysisofoperators AT rodinoluigi timefrequencyanalysisofoperators AT walterdegruytergmbhcokg timefrequencyanalysisofoperators |