Laguerre calculus and its applications on the Heisenberg Group:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
2001
|
| Series: | AMS, IP studies in advanced mathematics
22 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 319 S. |
| ISBN: | 0821827618 |
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MARC
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| 245 | 1 | 0 | |a Laguerre calculus and its applications on the Heisenberg Group |c Carlos Berenstein ; Der-Chen Chang ; Jingzhi Tie |
| 264 | 1 | |a Providence, RI |b AMS |c 2001 | |
| 300 | |a XII, 319 S. | ||
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| 490 | 1 | |a AMS, IP studies in advanced mathematics |v 22 | |
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| 650 | 4 | |a Laguerre, Polynômes de | |
| 650 | 4 | |a Calculus, Operational | |
| 650 | 4 | |a Laguerre polynomials | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface x;
1 The Laguerre Calculus 1
1.1 The Heisenberg group 1
1.2 The twisted and P.V. convolution operators 2
1.3 Laguerre calculus 6
2 Estimates for Powers of the Sub Laplacian 33
2.1 Introduction 33
2.2 The powers of the sub Laplacian 37
2.3 The heat kernel 40
2.4 Estimates of Pm in Hardy spaces 44
2.5 BMO estimates for the operator $m 55
2.6 The Riesz transforms on Hn 58
2.7 Connection with R2ra 68
3 Estimates for the Spectrum Projection Operators of the
Sub Laplacian 77
3.1 The Lp spectrum of (£, iT) 77
3.2 Estimates for the operator T^£ in Morrey spaces 84
3.3 The spectral projection operator 89
3.4 The Schrodinger operator 94
3.5 The fundamental solution of Aa,« 96
3.6 Estimate db operator in Morrey space 102
Appendix: The Isotropic Heisenberg Group 105
4 Inverse of the Operator ?„ = E =i(Xj Xj+J 2ioT 111
4.1 Introduction Ill
4.2 Inverting aQ: symbols 112
4.3 Inverting na: the kernel 124
4.4 Real a : Miiller and Ricci s result 135
4.5 The wave equation on the Heisenberg group 139
ix
x CONTENTS
5 The explict solution of the 9 Neumann problem in a non
isotropic Siegel domain 151
5.1 Introduction 151
5.2 d operators and d Laplacian on lAn 152
5.3 The Laguerre calculus on Hn x Rd 156
5.4 The Fundamental solution of oa 158
5.5 5 Neumann problem 162
5.6 The associated heat equation 166
5.7 The Laplacian operator on the Heisenberg group 176
6 Injectivity of the Pompeiu Transform in the Isotropic Hn 185
6.1 Introduction 185
6.2 Preliminaries 186
6.3 The group algebras £j(Hn) and Lj(Hn) 188
6.4 Description of U(n) and T spherical functions and the spaces
m* and Tl 191
6.5 Convolution equations systems with 0 and O homogeneous
compactly supported Radon measures as coefficients 210
6.6 Pompeiu type theorems in Hn 216
6.7 The interpretation from the point of view of the Weyl func¬
tional calculus 223
7 Morera type Theorems for Holomorphic W Spaces in Hn (I) 229
7.1 Introduction 229
7.2 Boundary analogues of the Morera theorem A Morera type
theorem for CR functions in the class L2(Hn) 234
7.3 A Morera type theorem for CR functions on the unit ball . . 247
8 Morera type Theorems for Holomorphic W Spaces in Hn
(II) 257
8.1 m homogeneous and m homogeneous functions on Hn .... 258
8.2 The subalgebra Loo(Hn) and convolution equations for m
homogeneous functions 290
8.3 Morera type theorems for Ti.p(Hn) spaces in Hn 300
8.4 The characterization of H°°{dMn+1) via Morera theorems .. 314
|
| any_adam_object | 1 |
| author | Berenstein, Carlos A. 1944-2019 Chang, Der-Chen Tie, Jingzhi |
| author_GND | (DE-588)130607010 |
| author_facet | Berenstein, Carlos A. 1944-2019 Chang, Der-Chen Tie, Jingzhi |
| author_role | aut aut aut |
| author_sort | Berenstein, Carlos A. 1944-2019 |
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| building | Verbundindex |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)45636925 (DE-599)BVBBV013859146 |
| dewey-full | 515/.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.72 |
| dewey-search | 515/.72 |
| dewey-sort | 3515 272 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013859146 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:53:17Z |
| institution | BVB |
| isbn | 0821827618 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009478709 |
| oclc_num | 45636925 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XII, 319 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | AMS |
| record_format | marc |
| series | AMS, IP studies in advanced mathematics |
| series2 | AMS, IP studies in advanced mathematics |
| spelling | Berenstein, Carlos A. 1944-2019 Verfasser (DE-588)130607010 aut Laguerre calculus and its applications on the Heisenberg Group Carlos Berenstein ; Der-Chen Chang ; Jingzhi Tie Providence, RI AMS 2001 XII, 319 S. txt rdacontent n rdamedia nc rdacarrier AMS, IP studies in advanced mathematics 22 Calcul symbolique Groupes de Lie nilpotents Laguerre, Polynômes de Calculus, Operational Laguerre polynomials Nilpotent Lie groups Nilpotente Lie-Gruppe (DE-588)4475237-4 gnd rswk-swf Laguerre-Polynome (DE-588)4293931-8 gnd rswk-swf Operatorenrechnung (DE-588)4389717-4 gnd rswk-swf Laguerre-Polynome (DE-588)4293931-8 s Operatorenrechnung (DE-588)4389717-4 s Nilpotente Lie-Gruppe (DE-588)4475237-4 s DE-604 Chang, Der-Chen Verfasser aut Tie, Jingzhi Verfasser aut AMS, IP studies in advanced mathematics 22 (DE-604)BV011103148 22 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009478709&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berenstein, Carlos A. 1944-2019 Chang, Der-Chen Tie, Jingzhi Laguerre calculus and its applications on the Heisenberg Group AMS, IP studies in advanced mathematics Calcul symbolique Groupes de Lie nilpotents Laguerre, Polynômes de Calculus, Operational Laguerre polynomials Nilpotent Lie groups Nilpotente Lie-Gruppe (DE-588)4475237-4 gnd Laguerre-Polynome (DE-588)4293931-8 gnd Operatorenrechnung (DE-588)4389717-4 gnd |
| subject_GND | (DE-588)4475237-4 (DE-588)4293931-8 (DE-588)4389717-4 |
| title | Laguerre calculus and its applications on the Heisenberg Group |
| title_auth | Laguerre calculus and its applications on the Heisenberg Group |
| title_exact_search | Laguerre calculus and its applications on the Heisenberg Group |
| title_full | Laguerre calculus and its applications on the Heisenberg Group Carlos Berenstein ; Der-Chen Chang ; Jingzhi Tie |
| title_fullStr | Laguerre calculus and its applications on the Heisenberg Group Carlos Berenstein ; Der-Chen Chang ; Jingzhi Tie |
| title_full_unstemmed | Laguerre calculus and its applications on the Heisenberg Group Carlos Berenstein ; Der-Chen Chang ; Jingzhi Tie |
| title_short | Laguerre calculus and its applications on the Heisenberg Group |
| title_sort | laguerre calculus and its applications on the heisenberg group |
| topic | Calcul symbolique Groupes de Lie nilpotents Laguerre, Polynômes de Calculus, Operational Laguerre polynomials Nilpotent Lie groups Nilpotente Lie-Gruppe (DE-588)4475237-4 gnd Laguerre-Polynome (DE-588)4293931-8 gnd Operatorenrechnung (DE-588)4389717-4 gnd |
| topic_facet | Calcul symbolique Groupes de Lie nilpotents Laguerre, Polynômes de Calculus, Operational Laguerre polynomials Nilpotent Lie groups Nilpotente Lie-Gruppe Laguerre-Polynome Operatorenrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009478709&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011103148 |
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