Pseudodifferential Analysis on Symmetric Cones: 22 (Studies in Advanced Mathematics) - Hardcover

Unterberger, Andre; Upmeier, Harald

Hardcover

ISBN 10: 0849378737 ISBN 13: 9780849378737

Publisher: CRC Press, 1995

Synopsis

Symmetric cones, possibly disguised under non-linear changes of coordinates, are the building blocks of manifolds with edges, corners, or conical points of a very general nature. Besides being a canonical open set of some Euclidean space, a symmetric cone L has an intrinsic Riemannian structure of its own, turning it into a symmetric space. These two structures make it possible to define on L a pseudodifferential analysis (the Fuchs calculus). The considerable interest in pseudodifferential problems on manifolds with non-smooth boundaries makes the precise analyses presented in this book both interesting and important. Much of the material in this book has never been previously published.
The methods used throughout the text rely heavily on the use of tools from quantum mechanics, such as representation theory and coherent states. Classes of operators defined by their symbols are given intrinsic characterizations. Harmonic analysis is discussed via the automorphism group of the complex tube over L.
The basic definitions governing the Fuchs calculus are provided, and a thorough exposition of the fundamental facts concerning the geometry of symmetric cones is given. The relationship with Jordan algebras is outlined and the general theory is illustrated by numerous examples.
The book offers the reader the technical tools for proving the main properties of the Fuchs calculus, with an emphasis on using the non-Euclidean Riemannian structure of the underlying cone. The fundamental results of pseudodifferential analysis are presented. The authors also develop the relationship to complex analysis and group representation.
This book benefits researchers interested in analysis on non-smooth domains or anyone working in pseudodifferential analysis. People interested in the geometry or harmonic analysis of symmetric cones will find in this valuable reference a new range of applications of complex analysis on tube-type symmetric domains and of the theory of Jordan algebras.

About this title

From the Back Cover

This monograph is intended for use by researchers in pseudodifferential analysis. While the emphasis is mainly on analysis on nonsmooth domains the precision of the methods should be of interest to anyone working in pseudodifferential analysis. Also people interested in the geometry or harmonic analysis of symmetric cones will find here a new range of applications of complex analysis on tube-type symmetric domains and of the theory of Jordan algebras.

About this edition

• Publisher: CRC Press
• Publication date: 1995
• ISBN 10: 0849378737
• ISBN 13: 9780849378737
• Binding: Hardcover
• Edition number: 1
• Number of pages: 224