Lectures on Hermite and Laguerre expansions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton Univ. Press
1993
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| Schriftenreihe: | Mathematical notes
42 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 195 S. |
| ISBN: | 0691000484 |
Internformat
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Datensatz im Suchindex
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| adam_text | CONTENTS
Preface ix
Acknowledgements xv
Chapter 1. Hennite, Special Hermite and Laguerre Functions
§1.1 Hermite and Laguerre Functions 1
§1.2 Heisenberg Group and Weyl Transform 9
§1.3 Special Hermite Functions 14
§1.4 Hermite and Laguerre Functions on the Heisenberg Group 22
§1.5 Asymptotic Properties of Hermite and Laguerre Functions 26
Chapter 2. Special Hermite Expansions
§2.1 Special Hermite Expansions 29
§2.2 Oscillatory Singular Integrals and Riesz Transforms 32
§2.3 Littlewood Paley Stein Theory 39
§2.4 Multipliers for Special Hermite Expansions 45
§2.5 Riesz Means for Special Hermite Expansions 51
§2.6 Proof of the Restriction Theorem 59
Chapter 3. Multiple Hermite Expansions
§3.1 Riesz Means and the Critical Index 65
§3.2 An L2 Estimate for the Riesz Kernel 69
§3.3 Almost Everywhere and Mean Summability 77
§3.4 Hermite Expansions for Radial Functions 81
Chapter 4. Multipliers for Hermite Expansions
§4.1 Littlewood Paley Stein Theory for the Hermite Semigroup 85
§4.2 Marcinkiewicz Multiplier Theorem 90
§4.3 Conjugate Poisson Integrals and Riesz Transforms 94
§4.4 Wave Equation for the Hermite Operator 105
Chapter 5. Hermite Expansions on IR,
§5.1 Cesaro Means and the Critical Index 111
§5.2 An Expression for the Cesaro Kernel and the Basic Estimates 114
§5.3 Estimating the Oscillatory Integrals 119
§5.4 Almost Everywhere and Mean Summability Results 131
vii
viii CONTENTS
Chapter 6. Laguerre Expansions
§6.1 The Laguerre Convolution 137
§6.2 Laguerre Expansions of Convolution Type 143
§6.3 Standard Laguerre Expansions 150
§6.4 Laguerre Expansions of Hermite Type 156
Chapter 7. The Transplantation Theorems
§7.1 The Transplantation Operators 167
§7.2 Further Reduction in the Proof of the Propositions 171
§7.3 Some Preliminary Lemmas 176
§7.4 Estimating f, °+ie f 181
§7.5 Estimating f^+2+ief 186
Bibliography 193
|
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| author | Thangavelu, Sundaram 1957- |
| author_GND | (DE-588)120232383 |
| author_facet | Thangavelu, Sundaram 1957- |
| author_role | aut |
| author_sort | Thangavelu, Sundaram 1957- |
| author_variant | s t st |
| building | Verbundindex |
| bvnumber | BV008247502 |
| classification_rvk | SI 870 SK 260 |
| classification_tum | MAT 339f |
| ctrlnum | (OCoLC)246889996 (DE-599)BVBBV008247502 |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:17:04Z |
| institution | BVB |
| isbn | 0691000484 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005446054 |
| oclc_num | 246889996 |
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| physical | XV, 195 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series | Mathematical notes |
| series2 | Mathematical notes |
| spelling | Thangavelu, Sundaram 1957- Verfasser (DE-588)120232383 aut Lectures on Hermite and Laguerre expansions by Sundaram Thangavelu Princeton, NJ Princeton Univ. Press 1993 XV, 195 S. txt rdacontent n rdamedia nc rdacarrier Mathematical notes 42 Hermite-Polynome (DE-588)4293831-4 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Laguerre-Polynome (DE-588)4293931-8 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Hermite-Polynome (DE-588)4293831-4 s Laguerre-Polynome (DE-588)4293931-8 s Mathematical notes 42 (DE-604)BV000003793 42 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005446054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Thangavelu, Sundaram 1957- Lectures on Hermite and Laguerre expansions Mathematical notes Hermite-Polynome (DE-588)4293831-4 gnd Darstellungstheorie (DE-588)4148816-7 gnd Laguerre-Polynome (DE-588)4293931-8 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4293831-4 (DE-588)4148816-7 (DE-588)4293931-8 (DE-588)4072157-7 |
| title | Lectures on Hermite and Laguerre expansions |
| title_auth | Lectures on Hermite and Laguerre expansions |
| title_exact_search | Lectures on Hermite and Laguerre expansions |
| title_full | Lectures on Hermite and Laguerre expansions by Sundaram Thangavelu |
| title_fullStr | Lectures on Hermite and Laguerre expansions by Sundaram Thangavelu |
| title_full_unstemmed | Lectures on Hermite and Laguerre expansions by Sundaram Thangavelu |
| title_short | Lectures on Hermite and Laguerre expansions |
| title_sort | lectures on hermite and laguerre expansions |
| topic | Hermite-Polynome (DE-588)4293831-4 gnd Darstellungstheorie (DE-588)4148816-7 gnd Laguerre-Polynome (DE-588)4293931-8 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Hermite-Polynome Darstellungstheorie Laguerre-Polynome Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005446054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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