An introduction to frames and Riesz bases:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
[Basel]
Birkhäuser
[2016]
|
| Edition: | Second edition |
| Series: | Applied and numerical harmonic analysis
|
| Subjects: | |
| Online Access: | BTU01 FHR01 FRO01 TUM01 UBM01 UBT01 UBW01 UEI01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 1 Online-Ressource (XXV, 704 Seiten) Illustrationen, Diagramme |
| ISBN: | 9783319256139 |
| ISSN: | 2296-5009 |
| DOI: | 10.1007/978-3-319-25613-9 |
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Record in the Search Index
| _version_ | 1804176260719443968 |
|---|---|
| adam_text | AN INTRODUCTION TO FRAMES AND RIESZ BASES
/ CHRISTENSEN, OLE
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
FRAMES IN FINITE-DIMENSIONAL INNER PRODUCT SPACES
INFINITE-DIMENSIONAL VECTOR SPACES AND SEQUENCES
BASES
BASES AND THEIR LIMITATIONS
FRAMES IN HILBERT SPACES
TIGHT FRAMES AND DUAL FRAME PAIRS
FRAMES VERSUS RIESZ BASES
SELECTED TOPICS IN FRAME THEORY
FRAMES OF TRANSLATES
SHIFT-INVARIANT SYSTEMS IN L2(R)
GABOR FRAMES IN L2(R)
GABOR FRAMES AND DUALITY
SELECTED TOPICS ON GABOR FRAMES
GABOR FRAMES INℓ2(Z),L2(0,L),CL
GENERAL WAVELET FRAMES IN L2(R)
DYADIC WAVELET FRAMES FORL2(R)
FRAME MULTIRESOLUTION ANALYSIS
WAVELET FRAMES VIA EXTENSION PRINCIPLES
SELECTED TOPICS ON WAVELET FRAMES
GENERALIZED SHIFT-INVARIANT SYSTEMS INL2(RD)
FRAMES ON LOCALLY COMPACT ABELIAN GROUPS
PERTURBATION OF FRAMES
APPROXIMATION OF THE INVERSE FRAME OPERATOR
EXPANSIONS IN BANACH SPACES. APPENDIX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
AN INTRODUCTION TO FRAMES AND RIESZ BASES
/ CHRISTENSEN, OLE
: 2016
ABSTRACT / INHALTSTEXT
THIS REVISED AND EXPANDED MONOGRAPH PRESENTS THE GENERAL THEORY FOR
FRAMES AND RIESZ BASES IN HILBERT SPACES AS WELL AS ITS CONCRETE
REALIZATIONS WITHIN GABOR ANALYSIS, WAVELET ANALYSIS, AND GENERALIZED
SHIFT-INVARIANT SYSTEMS. COMPARED WITH THE FIRST EDITION, MORE
EMPHASIS IS PUT ON EXPLICIT CONSTRUCTIONS WITH ATTRACTIVE PROPERTIES.
BASED ON THE EXITING DEVELOPMENT OF FRAME THEORY OVER THE LAST DECADE,
THIS SECOND EDITION NOW INCLUDES NEW SECTIONS ON THE RAPIDLY GROWING
FIELDS OF LCA GROUPS, GENERALIZED SHIFT-INVARIANT SYSTEMS, DUALITY
THEORY FOR AS WELL GABOR FRAMES AS WAVELET FRAMES, AND OPEN PROBLEMS IN
THE FIELD. KEY FEATURES INCLUDE: *ELEMENTARY INTRODUCTION TO FRAME
THEORY IN FINITE-DIMENSIONAL SPACES * BASIC RESULTS PRESENTED IN AN
ACCESSIBLE WAY FOR BOTH PURE AND APPLIED MATHEMATICIANS * EXTENSIVE
EXERCISES MAKE THE WORK SUITABLE AS A TEXTBOOK FOR USE IN GRADUATE
COURSES * FULL PROOFS INCLUD ED IN INTRODUCTORY CHAPTERS; ONLY BASIC
KNOWLEDGE OF FUNCTIONAL ANALYSIS REQUIRED * EXPLICIT CONSTRUCTIONS OF
FRAMES AND DUAL PAIRS OF FRAMES, WITH APPLICATIONS AND CONNECTIONS TO
TIME-FREQUENCY ANALYSIS, WAVELETS, AND GENERALIZED SHIFT-INVARIANT
SYSTEMS * DISCUSSION OF FRAMES ON LCA GROUPS AND THE CONCRETE
REALIZATIONS IN TERMS OF GABOR SYSTEMS ON THE ELEMENTARY GROUPS;
CONNECTIONS TO SAMPLING THEORY * SELECTED RESEARCH TOPICS PRESENTED
WITH RECOMMENDATIONS FOR MORE ADVANCED TOPICS AND FURTHER READIN G *
OPEN PROBLEMS TO STIMULATE FURTHER RESEARCH AN INTRODUCTION TO FRAMES
AND RIESZ BASESWILL BE OF INTEREST TO GRADUATE STUDENTS AND
RESEARCHERS WORKING IN PURE AND APPLIED MATHEMATICS,MATHEMATICAL
PHYSICS, AND ENGINEERING. PROFESSIONALS WORKING IN DIGITAL SIGNAL
PROCESSING WHO WISH TO UNDERSTAND THE THEORY BEHIND MANY MODERN SIGNAL
PROCESSING TOOLS MAY ALSO FIND THIS BOOK A USEFUL SELF-STUDY REFERENCE.
REVIEW OF THE FIRST EDITION: OLE CHRISTENSEN’SAN INTRODUCTION TO
FRAMES AND RIESZ BASESIS A FIRST-RATE INTRODUCTION TO THE FIELD … .
THE BOOK PROVIDES AN EXCELLENT EXPOSITION OF THESE TOPICS. THE MATERIAL
IS BROAD ENOUGH TO PIQUE THE INTEREST OF MANY READERS, THE INCLUDED
EXERCISES SUPPLY SOME INTERESTING CHALLENGES, AND THE COVERAGE PROVIDES
ENOUGH BACKGROUND FOR THOSE NEW TO THE SUBJECT TO BEGIN CONDUCTING
ORIGINAL RESEARCH. — ERIC S. WEBER, AMERICAN MATHEMATICAL
MONTHLY, VOL. 112, FEBRUARY, 2005
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Christensen, Ole 1966- |
| author_GND | (DE-588)12445836X |
| author_facet | Christensen, Ole 1966- |
| author_role | aut |
| author_sort | Christensen, Ole 1966- |
| author_variant | o c oc |
| building | Verbundindex |
| bvnumber | BV043579521 |
| classification_rvk | SK 470 SK 600 SK 450 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (ZDB-2-SMA)978-3-319-25613-9 (OCoLC)951068705 (DE-599)BVBBV043579521 |
| 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 |
| doi_str_mv | 10.1007/978-3-319-25613-9 |
| edition | Second edition |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:29:22Z |
| institution | BVB |
| isbn | 9783319256139 |
| issn | 2296-5009 |
| language | English |
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| series2 | Applied and numerical harmonic analysis |
| spelling | Christensen, Ole 1966- (DE-588)12445836X aut An introduction to frames and Riesz bases Ole Christensen Second edition [Basel] Birkhäuser [2016] © 2016 1 Online-Ressource (XXV, 704 Seiten) Illustrationen, Diagramme txt rdacontent c rdamedia cr rdacarrier Applied and numerical harmonic analysis 2296-5009 Mathematics Harmonic analysis Functional analysis Operator theory Functional Analysis Abstract Harmonic Analysis Operator Theory Signal, Image and Speech Processing Mathematik Frame Mathematik (DE-588)4528312-6 gnd rswk-swf Riesz-Basis (DE-588)4688993-0 gnd rswk-swf Frame Mathematik (DE-588)4528312-6 s Riesz-Basis (DE-588)4688993-0 s DE-604 Erscheint auch als Druck-Ausgabe 978-3-319-25611-5 Erscheint auch als Druckausgabe 978-3-319-25611-5 https://doi.org/10.1007/978-3-319-25613-9 Verlag URL des Erstveröffentlichers Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028994194&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028994194&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Christensen, Ole 1966- An introduction to frames and Riesz bases Mathematics Harmonic analysis Functional analysis Operator theory Functional Analysis Abstract Harmonic Analysis Operator Theory Signal, Image and Speech Processing Mathematik Frame Mathematik (DE-588)4528312-6 gnd Riesz-Basis (DE-588)4688993-0 gnd |
| subject_GND | (DE-588)4528312-6 (DE-588)4688993-0 |
| title | An introduction to frames and Riesz bases |
| title_auth | An introduction to frames and Riesz bases |
| title_exact_search | An introduction to frames and Riesz bases |
| title_full | An introduction to frames and Riesz bases Ole Christensen |
| title_fullStr | An introduction to frames and Riesz bases Ole Christensen |
| title_full_unstemmed | An introduction to frames and Riesz bases Ole Christensen |
| title_short | An introduction to frames and Riesz bases |
| title_sort | an introduction to frames and riesz bases |
| topic | Mathematics Harmonic analysis Functional analysis Operator theory Functional Analysis Abstract Harmonic Analysis Operator Theory Signal, Image and Speech Processing Mathematik Frame Mathematik (DE-588)4528312-6 gnd Riesz-Basis (DE-588)4688993-0 gnd |
| topic_facet | Mathematics Harmonic analysis Functional analysis Operator theory Functional Analysis Abstract Harmonic Analysis Operator Theory Signal, Image and Speech Processing Mathematik Frame Mathematik Riesz-Basis |
| url | https://doi.org/10.1007/978-3-319-25613-9 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028994194&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028994194&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT christensenole anintroductiontoframesandrieszbases |