Harmonic Analysis on the Heisenberg Group

Dekorationsartikel gehören nicht zum Leistungsumfang.

Sprache: Englisch

108,95 €*

inkl. MwSt.

Versandkostenfrei per Post / DHL

Lieferzeit 1-2 Wochen

Kategorien:

Der Artikel ist nicht in deutscher Sprache verfasst.
Die Sprache der Produktbeschreibung und Details kann in Englisch angegeben sein. Sollten Sie Verständnisprobleme haben, wenden Sie sich gerne an uns.

Beschreibung

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. Thangavelüs 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.

Zusammenfassung

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. 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.

Inhaltsverzeichnis

1 The Group Fourier Transform.- 1.1 The Heisenberg group.- 1.2 The Schrödinger representations.- 1.3 The Fourier and Weyl transforms.- 1.4 Hermite and special Hermite functions.- 1.5 Paley-Wiener theorems for the Fourier transform.- 1.6 An uncertainty principle on the Heisenberg group.- 1.7 Notes and references.- 2 Analysis of the Sublaplacian.- 2.1 Spectral theory of the sublaplacian.- 2.2 Spectral decomposition for Lp functions.- 2.3 Restriction theorems for the spectral projections.- 2.4 A Paley-Wiener theorem for the spectral projections.- 2.5 Bochner-Riesz means for the sublaplacian.- 2.6 A multiplier theorem for the Fourier transform.- 2.7 Notes and references.- 3 Group Algebras and Applications.- 3.1 The Heisenberg motion group.- 3.2 Gelfand pairs, spherical functions and group algebras.- 3.3 An algebra of radial measures.- 3.4 Analogues of Wiener-Tauberian theorem.- 3.5 Spherical means on the Heisenberg group.- 3.6 A maximal theorem for spherical means.- 3.7 Notes and references.- 4 The Reduced Heisenberg Group.- 4.1 The reduced Heisenberg group.- 4.2 A Wiener-Tauberian theorem for Lp functions.- 4.3 A maximal theorem for spherical means.- 4.4 Mean periodic functions on phase space.- 4.5 Notes and references.

Details

Erscheinungsjahr:	1998
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Progress in Mathematics
Inhalt:	xii 195 S.
ISBN-13:	9780817640507
ISBN-10:	0817640509
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Thangavelu, Sundaram
Redaktion:	Thangavelu, Sundaram
Herausgeber:	Sundaram Thangavelu
Hersteller:	Birkhuser Boston Birkhäuser Boston Progress in Mathematics
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	241 x 160 x 16 mm
Von/Mit:	Sundaram Thangavelu
Erscheinungsdatum:	24.03.1998
Gewicht:	0,483 kg

Artikel-ID: 102889661

Zusammenfassung

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. 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.

Inhaltsverzeichnis

Details

Erscheinungsjahr:	1998
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Progress in Mathematics
Inhalt:	xii 195 S.
ISBN-13:	9780817640507
ISBN-10:	0817640509
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Thangavelu, Sundaram
Redaktion:	Thangavelu, Sundaram
Herausgeber:	Sundaram Thangavelu
Hersteller:	Birkhuser Boston Birkhäuser Boston Progress in Mathematics
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	241 x 160 x 16 mm
Von/Mit:	Sundaram Thangavelu
Erscheinungsdatum:	24.03.1998
Gewicht:	0,483 kg