Fourier analysis on finite Abelian groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2009
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| Schriftenreihe: | Applied and numerical harmonic analysis
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 156 S. 24 cm |
| ISBN: | 9780817649159 |
Internformat
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| 650 | 4 | |a Fourier analysis | |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS SERIES PREFACE IX PREFACE XIII OVERVIEW XV 1 FOUNDATION
MATERIAL 1 1.1 RESULTS FROM GROUP THEORY 1 1.2 QUADRATIC CONGRUENCES 10
1.3 CHEBYSHEV SYSTEMS OF FUNCTIONS 15 2 LINEAR ALGEBRA 23 2.1 INNER
PRODUCT SPACES 23 2.2 LINEAR FUNCTIONALS AND DUAL SPACES 26 2.3 A
SPECIAL CLASS OF LINEAR OPERATORS 29 3 CHARACTERS OF FINITE GROUPS 33
3.1 DEFINITION AND BASIC PROPERTIES OF CHARACTERS 33 3.2 THE ORTHOGONAL
RELATIONS FOR CHARACTERS 40 4 THE FOURIER TRANSFORM 49 4.1 DEFINITION
AND SOME PROPERTIES 49 4.2 THE FOURIER TRANSFORM OF PERIODIC FUNCTIONS
54 4.2.1 PERIODIC FUNCTIONS ON Z N 54 4.2.2 PERIODIC FUNCTIONS ON Z 57
4.3 THE INVERSE FOURIER TRANSFORM 58 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/995948488 DIGITALISIERT DURCH 155 VIII CONTENTS 4.4 THE
INVERSION FORMULA 59 4.5 MATRICES OF THE FOURIER TRANSFORM 61 4.6
ITERATED FOURIER TRANSFORMS 62 4.7 IS THE FOURIER TRANSFORM A
SELF-ADJOINT OPERATOR? . . 65 5 CONVOLUTION, BANACH ALGEBRAS, AND THE
UNCERTAINTY PRINCIPLE 67 5.1 THE CONVOLUTION OPERATOR 67 5.2 BANACH
ALGEBRA 73 5.3 THE UNCERTAINTY PRINCIPLE 76 6 A REDUCTION THEOREM 81 6.1
THE TENSOR DECOMPOSITION OF VECTOR SPACES 81 6.2 THE TENSOR
DECOMPOSITION OF THE FOURIER TRANSFORM 84 6.3 THE FOURIER TRANSFORM AND
ISOMET RIES 88 6.4 REDUCTION TO FINITE CYCLIC GROUPS 89 7 EIGENVALUES
AND EIGENVECTORS OF THE FOURIER TRANSFORM 93 7.1 SYMMETRIC AND
ANTISYMMETRIC FUNCTIONS 93 7.2 EIGENVALUES AND EIGENVECTORS 98 7.3
SPECTRAL THEOREM 104 7.4 ERGODIC THEOREM 109 7.5 MULTIPLICITIES OF
EIGENVALUES 112 8 THE QUANTUM FOURIER TRANSFORM 131 8.1 THE DIRAC
NOTATION 131 8.2 THE FOURIER TRANSFORM IN THE DIRAC NOTATION 134 9
QUADRATIC GAUSSIAN SUMS 141 9.1 THE NUMBER G N (L) 141 9.2 REDUCTION
FORMULAS 144 REFERENCES 153 INDEX
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:05:24Z |
| institution | BVB |
| isbn | 9780817649159 |
| language | English |
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| physical | XVI, 156 S. 24 cm |
| publishDate | 2009 |
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| series2 | Applied and numerical harmonic analysis |
| spelling | Luong, Bao Verfasser (DE-588)13943738X aut Fourier analysis on finite Abelian groups Bao Luong Boston [u.a.] Birkhäuser 2009 XVI, 156 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Applied and numerical harmonic analysis Fourier-Transformation Abelian groups Finite groups Fourier analysis Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 s DE-604 Erscheint auch als Online-Ausgabe 978-0-8176-4916-6 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018681094&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Luong, Bao Fourier analysis on finite Abelian groups Fourier-Transformation Abelian groups Finite groups Fourier analysis Fourier-Transformation (DE-588)4018014-1 gnd |
| subject_GND | (DE-588)4018014-1 |
| title | Fourier analysis on finite Abelian groups |
| title_auth | Fourier analysis on finite Abelian groups |
| title_exact_search | Fourier analysis on finite Abelian groups |
| title_full | Fourier analysis on finite Abelian groups Bao Luong |
| title_fullStr | Fourier analysis on finite Abelian groups Bao Luong |
| title_full_unstemmed | Fourier analysis on finite Abelian groups Bao Luong |
| title_short | Fourier analysis on finite Abelian groups |
| title_sort | fourier analysis on finite abelian groups |
| topic | Fourier-Transformation Abelian groups Finite groups Fourier analysis Fourier-Transformation (DE-588)4018014-1 gnd |
| topic_facet | Fourier-Transformation Abelian groups Finite groups Fourier analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018681094&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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