Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group

Valery V. Volchkov|Vitaly V. Volchkov

ISBN 10: 1848825323 / ISBN 13: 9781848825321

Published by Springer London, 2009

About this Item

Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. The approach employed in this book is the best suited for dealing with the subject in a systematic fashion.Most of the results are the best possible, giving answers to all questions that naturally arise in the topic and presenting the complete pic.

Seller Inventory # 4287048

Bibliographic Details

• Title: Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group
• Publisher: Springer London
• Publication Date: 2009
• Language: English
• ISBN 10: 1848825323
• ISBN 13: 9781848825321
• Binding: Hardcover
• Condition: New

About this title

Synopsis

The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years. There has been much progress in a number of problems concerning local - pects of spectral analysis and spectral synthesis on homogeneous spaces. The study oftheseproblemsturnsouttobecloselyrelatedtoavarietyofquestionsinharmonic analysis, complex analysis, partial differential equations, integral geometry, appr- imation theory, and other branches of contemporary mathematics. The present book describes recent advances in this direction of research. Symmetric spaces and the Heisenberg group are an active ?eld of investigation at 2 the moment. The simplest examples of symmetric spaces, the classical 2-sphere S 2 and the hyperbolic plane H , play familiar roles in many areas in mathematics. The n Heisenberg groupH is a principal model for nilpotent groups, and results obtained n forH may suggest results that hold more generally for this important class of Lie groups. The purpose of this book is to develop harmonic analysis of mean periodic functions on the above spaces.

From the Back Cover

This book presents the first systematic and unified treatment of the theory of mean periodic functions on homogeneous spaces. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to harmonic analysis, complex analysis, integral geometry, and analysis on symmetric spaces.

The main purpose of this book is the study of local aspects of spectral analysis and spectral synthesis on Euclidean spaces, Riemannian symmetric spaces of an arbitrary rank and Heisenberg groups.  The subject can be viewed as arising from three classical topics: John's support theorem, Schwartz's fundamental principle, and Delsarte's two-radii theorem.

Highly topical, the book contains most of the significant recent results in this area with complete and detailed proofs. In order to make this book accessible to a wide audience, the authors have included an introductory section that develops analysis on symmetric spaces without the use of Lie theory. Challenging open problems are described and explained, and promising new research directions are indicated.

Designed for both experts and beginners in the field, the book is rich in methods for a wide variety of problems in many areas of mathematics.