One-dimensional dyadic wavelets:
"The theory of wavelets has been thoroughly studied by many authors; standard references include books by I. Daubechies, by Y. Meyer, by R. Coifman and Y. Meyer, by C.K. Chui, and by M.V. Wickerhauser. In addition, the development of wavelets influenced the study of various other reproducing fu...
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| Main Authors: | , , , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2022
|
| Series: | Memoirs of the American Mathematical Society
Volume 280, Number 1378 (first of 8 numbers) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "The theory of wavelets has been thoroughly studied by many authors; standard references include books by I. Daubechies, by Y. Meyer, by R. Coifman and Y. Meyer, by C.K. Chui, and by M.V. Wickerhauser. In addition, the development of wavelets influenced the study of various other reproducing function systems. Interestingly enough, some open questions remained unsolved or only partially solved for more than twenty years even in the most basic case of dyadic orthonormal wavelets in a single dimension. These include issues related to the MRA structure (for example, a complete understanding of filters), the structure of the space of negative dilates (in particular, with respect to what is known as the Baggett problem), and the variety of resolution structures that may occur. In this article we offer a comprehensive, yet technically fairly elementary approach to these questions. On this path, we present a multitude of new results, resolve some of the old questions, and provide new advances for some problems that remain open for the future"-- |
| Item Description: | Includes bibliographical references "November 2022, volume 280, number 1378 (first of 8 numbers)" |
| Physical Description: | ix, 152 Seiten Diagramme |
| ISBN: | 9781470453749 |
Staff View
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Record in the Search Index
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| adam_text | Contents Chapter 1. 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. Principal Shift-Invariant Spaces: Preliminaries and Auxiliary Results 1 Basic Notions and Set Inclusion Relationship Between Two PrincipalShift-Invariant Spaces Three Types of Principal Shift-Invariant Spaces Coefficients Maximal Principal Shift-invariant Spaces Direct Analysis Sum Redundancy Remarks 1 7 12 15 20 27 33 Chapter 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. 2.8. 2.9. 2. MRA Structure Dilations and Shift-invariant Spaces Dilation Invariances Filter Analysis, FO Case. Smith-Barnwell Filters, FO Case Multiplicative Structure in the Classof FO Filters Structure of D((y?)): FO Case Pre-GMRA Filter Analysis, Non-FO Case Pre-GMRA Core 37 37 47 58 73 92 97 112 118 128 Chapter 3.1. 3.2. 3.3. 3. Wavelet Structure The Space of Negative Dilates Orthogonality General Case 133 133 137 145 Bibliography 149
|
| adam_txt |
Contents Chapter 1. 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. Principal Shift-Invariant Spaces: Preliminaries and Auxiliary Results 1 Basic Notions and Set Inclusion Relationship Between Two PrincipalShift-Invariant Spaces Three Types of Principal Shift-Invariant Spaces Coefficients Maximal Principal Shift-invariant Spaces Direct Analysis Sum Redundancy Remarks 1 7 12 15 20 27 33 Chapter 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. 2.8. 2.9. 2. MRA Structure Dilations and Shift-invariant Spaces Dilation Invariances Filter Analysis, FO Case. Smith-Barnwell Filters, FO Case Multiplicative Structure in the Classof FO Filters Structure of D((y?)): FO Case Pre-GMRA Filter Analysis, Non-FO Case Pre-GMRA Core 37 37 47 58 73 92 97 112 118 128 Chapter 3.1. 3.2. 3.3. 3. Wavelet Structure The Space of Negative Dilates Orthogonality General Case 133 133 137 145 Bibliography 149 |
| any_adam_object | 1 |
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| author | Luthy, Peter M. 1983- Šikić, Hrvoje Soria de Diego, Fernando Weiss, Guido L. 1928-2022 Wilson, Edward N. |
| author_GND | (DE-588)113206838X (DE-588)1299389252 (DE-588)1228303916 (DE-588)172446260 (DE-588)129938966X |
| author_facet | Luthy, Peter M. 1983- Šikić, Hrvoje Soria de Diego, Fernando Weiss, Guido L. 1928-2022 Wilson, Edward N. |
| author_role | aut aut aut aut aut |
| author_sort | Luthy, Peter M. 1983- |
| author_variant | p m l pm pml h š hš d d f s ddf ddfs g l w gl glw e n w en enw |
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| bvnumber | BV048684486 |
| ctrlnum | (OCoLC)1365560364 (DE-599)KXP1832134172 |
| dewey-full | 515/.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.2433 |
| dewey-search | 515/.2433 |
| dewey-sort | 3515 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV048684486 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T21:26:10Z |
| indexdate | 2024-07-10T09:46:02Z |
| institution | BVB |
| isbn | 9781470453749 |
| language | English |
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| physical | ix, 152 Seiten Diagramme |
| publishDate | 2022 |
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| spelling | Luthy, Peter M. 1983- (DE-588)113206838X aut One-dimensional dyadic wavelets Peter M. Luthy ; Hrvoje Šikić ; Fernando Soria ; Guido L. Weiss ; Edward N. Wilson Providence, RI American Mathematical Society 2022 © 2022 ix, 152 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society Volume 280, Number 1378 (first of 8 numbers) Includes bibliographical references "November 2022, volume 280, number 1378 (first of 8 numbers)" "The theory of wavelets has been thoroughly studied by many authors; standard references include books by I. Daubechies, by Y. Meyer, by R. Coifman and Y. Meyer, by C.K. Chui, and by M.V. Wickerhauser. In addition, the development of wavelets influenced the study of various other reproducing function systems. Interestingly enough, some open questions remained unsolved or only partially solved for more than twenty years even in the most basic case of dyadic orthonormal wavelets in a single dimension. These include issues related to the MRA structure (for example, a complete understanding of filters), the structure of the space of negative dilates (in particular, with respect to what is known as the Baggett problem), and the variety of resolution structures that may occur. In this article we offer a comprehensive, yet technically fairly elementary approach to these questions. On this path, we present a multitude of new results, resolve some of the old questions, and provide new advances for some problems that remain open for the future"-- Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Wavelets (Mathematics) Harmonic analysis Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systems Wavelet (DE-588)4215427-3 s Harmonische Analyse (DE-588)4023453-8 s DE-604 Šikić, Hrvoje (DE-588)1299389252 aut Soria de Diego, Fernando (DE-588)1228303916 aut Weiss, Guido L. 1928-2022 (DE-588)172446260 aut Wilson, Edward N. (DE-588)129938966X aut Erscheint auch als Online-Ausgabe 978-1-4704-7278-8 Memoirs of the American Mathematical Society Volume 280, Number 1378 (first of 8 numbers) (DE-604)BV008000141 1378 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034058793&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Luthy, Peter M. 1983- Šikić, Hrvoje Soria de Diego, Fernando Weiss, Guido L. 1928-2022 Wilson, Edward N. One-dimensional dyadic wavelets Memoirs of the American Mathematical Society Harmonische Analyse (DE-588)4023453-8 gnd Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4215427-3 |
| title | One-dimensional dyadic wavelets |
| title_auth | One-dimensional dyadic wavelets |
| title_exact_search | One-dimensional dyadic wavelets |
| title_exact_search_txtP | One-dimensional dyadic wavelets |
| title_full | One-dimensional dyadic wavelets Peter M. Luthy ; Hrvoje Šikić ; Fernando Soria ; Guido L. Weiss ; Edward N. Wilson |
| title_fullStr | One-dimensional dyadic wavelets Peter M. Luthy ; Hrvoje Šikić ; Fernando Soria ; Guido L. Weiss ; Edward N. Wilson |
| title_full_unstemmed | One-dimensional dyadic wavelets Peter M. Luthy ; Hrvoje Šikić ; Fernando Soria ; Guido L. Weiss ; Edward N. Wilson |
| title_short | One-dimensional dyadic wavelets |
| title_sort | one dimensional dyadic wavelets |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Harmonische Analyse Wavelet |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034058793&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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