Harmonic analysis: smooth and non-smooth
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2018]
|
| Series: | Regional conference series in mathematics
number 128 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 266 Seiten Illustrationen |
| ISBN: | 9781470448806 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface ix
Acknowledgments xi
Chapter 1. Introduction. Smooth vs the non-smooth categories 1
1.1. Preview 1
1.2. Historical context 3
1.3. Iterated function systems (IFS) 7
1.4. Frequency bands, filters, and representations of the Cuntz-algebras 13
1.5. Frames 16
1.6. Key themes in the book 17
Chapter 2. Spectral pair analysis for IFSs 23
2.1. The scale-4 Cantor measure, and its harmonic analysis 23
2.2. The middle third Cantor measure 27
2.3. Infinite Bernoulli convolutions 29
2.4. The scale-4 Cantor measure, and scaling by 5 in the spectrum 33
2.5. IFS measures and admissible harmonic analyses 37
2.6. Harmonic analysis of IFS systems with overlap 38
Chapter 3. Harmonic analyses on fractals, with an emphasis on iterated
function systems (IFS) measures 45
3.1. Harmonic analysis in the smooth vs the non-smooth categories 45
3.2. Spectral pairs and the Fuglede conjecture 46
3.3. Spectral pairs 51
3.4. Spectral theory of multiple intervals 58
Chapter 4. Four kinds of harmonic analysis 69
4.1. Orthogonal Fourier expansions 69
4.2. Frame and related non-orthogonal Fourier expansions 73
4.3. Wavelet expansions 79
4.4. Harmonic analysis via reproducing kernel Hilbert spaces (RKHS) 98
Chapter 5. Harmonic analysis via representations of the Cuntz relations 135
5.1. From frequency band filters to signals and to wavelet expansions 136
5.2. Stochastic processes via representations of the Cuntz relations 141
5.3. Representations in a universal Hilbert space 165
Chapter 6. Positive definite functions and kernel analysis 175
6.1. Positive definite kernels and harmonic analysis in T2(/x) when p
is a gap IFS fractal measure 175
vii
CONTENTS
vili
6.2. Positive definite kernels and harmonic analysis in L2 (/1) when /x
is a general singular measure in a finite interval 180
6.3. Positive definite kernels and the associated Gaussian processes 211
Chapter 7. Representations of Lie groups. Non-commutative harmonic
analysis 219
7.1. Fundamental domains as non-commutative tiling constructions 220
7.2. Symmetry for unitary representations of Lie groups 226
7.3. Symmetry in physics and reflection positive constructions via
unitary representations of Lie groups 241
Bibliography 245
Index 265
|
| any_adam_object | 1 |
| author | Jørgensen, Palle E. T. 1947- |
| author_GND | (DE-588)124805515 |
| author_facet | Jørgensen, Palle E. T. 1947- |
| author_role | aut |
| author_sort | Jørgensen, Palle E. T. 1947- |
| author_variant | p e t j pet petj |
| building | Verbundindex |
| bvnumber | BV045489878 |
| classification_rvk | SK 130 SI 195 SK 340 |
| ctrlnum | (OCoLC)1083860540 (DE-599)BVBBV045489878 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV045489878 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:19:29Z |
| institution | BVB |
| isbn | 9781470448806 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030874780 |
| oclc_num | 1083860540 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-188 DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-188 DE-19 DE-BY-UBM |
| physical | xi, 266 Seiten Illustrationen |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Regional conference series in mathematics |
| series2 | Regional conference series in mathematics |
| spelling | Jørgensen, Palle E. T. 1947- Verfasser (DE-588)124805515 aut Harmonic analysis smooth and non-smooth Palle E.T. Jorgensen Providence, Rhode Island American Mathematical Society [2018] © 2018 xi, 266 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Regional conference series in mathematics number 128 Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 Regional conference series in mathematics number 128 (DE-604)BV000004346 128 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030874780&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jørgensen, Palle E. T. 1947- Harmonic analysis smooth and non-smooth Regional conference series in mathematics Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 |
| title | Harmonic analysis smooth and non-smooth |
| title_auth | Harmonic analysis smooth and non-smooth |
| title_exact_search | Harmonic analysis smooth and non-smooth |
| title_full | Harmonic analysis smooth and non-smooth Palle E.T. Jorgensen |
| title_fullStr | Harmonic analysis smooth and non-smooth Palle E.T. Jorgensen |
| title_full_unstemmed | Harmonic analysis smooth and non-smooth Palle E.T. Jorgensen |
| title_short | Harmonic analysis |
| title_sort | harmonic analysis smooth and non smooth |
| title_sub | smooth and non-smooth |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Harmonische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030874780&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004346 |
| work_keys_str_mv | AT jørgensenpalleet harmonicanalysissmoothandnonsmooth |