β Scribed by Mikhail A. Shubin (auth.)
No coin nor oath required. For personal study only.
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.
Front Matter....Pages I-XII
Foundations of Ξ¨DO Theory....Pages 1-75
Complex Powers of Elliptic Operators....Pages 77-131
Asymptotic Behaviour of the Spectral Function....Pages 133-173
Pseudodifferential Operators in β n ....Pages 175-228
Back Matter....Pages 229-288
Analysis;Differential Geometry;Theoretical, Mathematical and Computational Physics
π SIMILAR VOLUMES
Provides an introduction to the theory of pseudodifferential operators and Fourier integral operators from the very basics. Written for a wide audience of mathematicians, be they interested students or researchers. Softcover.
Provides an introduction to the theory of pseudodifferential operators and Fourier integral operators from the very basics. Written for a wide audience of mathematicians, be they interested students or researchers. Softcover.
<p>I have tried in this book to describe those aspects of pseudodifferential and Fourier integral operator theory whose usefulness seems proven and which, from the viewpoint of organization and "presentability," appear to have stabilized. Since, in my opinion, the main justification for studying the
In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book
In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book