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An Introduction to Semiclassical and Microlocal Analysis : Universitext - Andre Bach

An Introduction to Semiclassical and Microlocal Analysis



Published: 2nd January 2002
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This book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical way and is mainly addressed to non-specialists in the subject. Both the standard Ci pseudodifferential calculus and the analytic microlocal analysis are developed, while the author replaces the delicate local theory with a more straightforward global theory. The book is based on lectures taught by the author over several years. Many exercises provide outlines of useful applications of the semi-classical theory and the only prerequisite required is a basic knowledge of the theory of distributions.

From the reviews:

"The book is very clearly written, and is indeed much simpler than most of others. ... this is an excellent book, suitable even for students with a poor background in the subject. In my opinion, every department offering courses on partial differential equations or asymptotic analysis should have it in the library. It will be very useful to all mathematicians working in semi-classical or microlocal analysis ... ." (Yuri Safarov, Bulletin of the London Mathematical Society, Issue 35, 2003)

"This is a concise and accessible book on the basic techniques of semiclassical and microlocal analysis. ... An appendix provides a useful summary of the major formulas used in the text. Each chapter is followed by a collection of provocative and well chosen exercises. The exercises are essential for understanding the work and provide important applications. ... the text does provide a very readable, clear, and concise introduction to semiclassical and microlocal analysis." (Peter D. Hislop, Mathematical Reviews, 2003 b)

"The contents of the book correspond to a course at Ph. D. Level, given by the author at the Universities of Bologna and Paris-Nord. ... the book collects in an original way standard results and new aspects of semi-classical microlocal analysis; the reading is suggested to non-specialists as well." (L. Rodino, Zentralblatt MATH, Vol. 994 (19), 2002)

"This book presents most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. ... The originality lies in the fact that the main features of analytic microlocal analysis are derived from a single and elementary a priori estimate. Various exercises illustrate the chief results of each chapter while introducing the reader to further developments of the theory. Applications to the study of the Schroedinger operator are also discussed, to further the understanding of new notions ... ." (L' Enseignement Mathematique, Vol. 48 (1-2), 2002)

"The book under review consists of lecture notes corresponding to a course taught for several years at the universities of Paris-Nord (France) and Bologna (Italy). It is addressed mainly to non-specialists in the subject, and the prerequisites are essentially reduced to the basic notions of the theory of distributions. ... The author tries to make clear how the things work and show examples where they can be applied. It is nicely written ... . the book can be highly recommended." (J. Synnatzschke, Zeitschrift fur Analysis und ihre Anwendungen - ZAA, Vol. 21 (3), 2002)

Introductionp. 1
Semiclassical Pseudodifferential Calculusp. 9
Microlocalizationp. 69
Applications to the Solutions of Analytic Linear PDEsp. 105
Complements: Symplectic Aspectsp. 141
Appendix: List of Formulaep. 169
Bibliographyp. 175
Indexp. 183
List of Notationp. 189
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387953441
ISBN-10: 0387953442
Series: Universitext
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 191
Published: 2nd January 2002
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.27
Weight (kg): 0.47