Pseudodifferential Operators and Spectral Theory (Springer Series in Soviet Mathematics) - Softcover

Shubin, M.A.

Softcover

ISBN 10: 354041195X ISBN 13: 9783540411956

Publisher: Springer, 2001

Synopsis

I had mixed feelings when I thought how I should prepare the book for the second edition. It was clear to me that I had to correct all mistakes and misprints that were found in the book during the life of the first edition. This was easy to do because the mistakes were mostly minor and easy to correct, and the misprints were not many. It was more difficult to decide whether I should update the book (or at least its bibliography) somehow. I decided that it did not need much of an updating. The main value of any good mathematical book is that it teaches its reader some language and some skills. It can not exhaust any substantial topic no matter how hard the author tried. Pseudodifferential operators became a language and a tool of analysis of partial differential equations long ago. Therefore it is meaningless to try to exhaust this topic. Here is an easy proof. As of July 3, 2000, MathSciNet (the database of the American Mathematical Society) in a few seconds found 3695 sources, among them 363 books, during its search for "pseudodifferential operator". (The search also led to finding 963 sources for "pseudo-differential operator" but I was unable to check how much the results ofthese two searches intersected). This means that the corresponding words appear either in the title or in the review published in Mathematical Reviews.

About this title

Review

From the reviews of the second edition:

"This is the second edition of Shubin’s already classical book. It provides a fairly short, highly readable nice introduction to microlocal analysis, with emphasis on its application to spectral theory ... . For anybody who holds a first course in PDO and FIO we highly recommend ... . The book is very well written, in simple and direct language. From the very basics at the beginning, the reader reaches a fairly advanced graduate level at the end." (Tibor Ódor, Acta Scientiarum Mathematicarum, Vol. 73, 2007)

Synopsis

This is the second edition of Shubin's classical book. It provides an introduction to the theory of pseudodifferential operators and Fourier integral operators from the very basics. The applications discussed include complex powers of elliptic operators, Hormander asymptotics of the spectral function and eigenvalues, and methods of approximate spectral projection. Exercises and problems are included to help the reader master the essential techniques. The book is written for a wide audience of mathematicians, be they interested students or researchers.

Edition details

• Publisher: Springer
• Publication date: 2001
• Language: English
• ISBN 10: 354041195X
• ISBN 13: 9783540411956
• Binding: Paperback
• Edition number: 2
• Number of pages: 300