Harmonic Analysis on the Heisenberg Group:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser Boston
1998
|
| Series: | Progress in Mathematics
159 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and hence gives the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Several results in this monograph appear for the first time in book form, and some theorems have not appeared elsewhere. The detailed discussion of the representation theory of the Heisenberg group goes well beyond the basic Stone-von Neumann theory, and its relations to classical special functions is invaluable for any reader interested in this group. Topic covered include the Plancherel and Paley—Wiener theorems, spectral theory of the sublaplacian, Wiener-Tauberian theorems, Bochner—Riesz means and multipliers for the Fourier transform. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable |
| Physical Description: | 1 Online-Ressource (XII, 195 p) |
| ISBN: | 9781461217725 9781461272755 |
| DOI: | 10.1007/978-1-4612-1772-5 |
Staff View
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| 500 | |a The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and hence gives the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Several results in this monograph appear for the first time in book form, and some theorems have not appeared elsewhere. The detailed discussion of the representation theory of the Heisenberg group goes well beyond the basic Stone-von Neumann theory, and its relations to classical special functions is invaluable for any reader interested in this group. Topic covered include the Plancherel and Paley—Wiener theorems, spectral theory of the sublaplacian, Wiener-Tauberian theorems, Bochner—Riesz means and multipliers for the Fourier transform. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable | ||
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| id | DE-604.BV042419910 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461217725 9781461272755 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855327 |
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| physical | 1 Online-Ressource (XII, 195 p) |
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| spelling | Thangavelu, Sundaram Verfasser aut Harmonic Analysis on the Heisenberg Group by Sundaram Thangavelu Boston, MA Birkhäuser Boston 1998 1 Online-Ressource (XII, 195 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 159 The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and hence gives the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Several results in this monograph appear for the first time in book form, and some theorems have not appeared elsewhere. The detailed discussion of the representation theory of the Heisenberg group goes well beyond the basic Stone-von Neumann theory, and its relations to classical special functions is invaluable for any reader interested in this group. Topic covered include the Plancherel and Paley—Wiener theorems, spectral theory of the sublaplacian, Wiener-Tauberian theorems, Bochner—Riesz means and multipliers for the Fourier transform. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable Mathematics Group theory Harmonic analysis Abstract Harmonic Analysis Group Theory and Generalizations Mathematik Heisenberg-Gruppe (DE-588)4314104-3 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Heisenberg-Gruppe (DE-588)4314104-3 s Harmonische Analyse (DE-588)4023453-8 s 1\p DE-604 https://doi.org/10.1007/978-1-4612-1772-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Thangavelu, Sundaram Harmonic Analysis on the Heisenberg Group Mathematics Group theory Harmonic analysis Abstract Harmonic Analysis Group Theory and Generalizations Mathematik Heisenberg-Gruppe (DE-588)4314104-3 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4314104-3 (DE-588)4023453-8 |
| title | Harmonic Analysis on the Heisenberg Group |
| title_auth | Harmonic Analysis on the Heisenberg Group |
| title_exact_search | Harmonic Analysis on the Heisenberg Group |
| title_full | Harmonic Analysis on the Heisenberg Group by Sundaram Thangavelu |
| title_fullStr | Harmonic Analysis on the Heisenberg Group by Sundaram Thangavelu |
| title_full_unstemmed | Harmonic Analysis on the Heisenberg Group by Sundaram Thangavelu |
| title_short | Harmonic Analysis on the Heisenberg Group |
| title_sort | harmonic analysis on the heisenberg group |
| topic | Mathematics Group theory Harmonic analysis Abstract Harmonic Analysis Group Theory and Generalizations Mathematik Heisenberg-Gruppe (DE-588)4314104-3 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Mathematics Group theory Harmonic analysis Abstract Harmonic Analysis Group Theory and Generalizations Mathematik Heisenberg-Gruppe Harmonische Analyse |
| url | https://doi.org/10.1007/978-1-4612-1772-5 |
| work_keys_str_mv | AT thangavelusundaram harmonicanalysisontheheisenberggroup |