Pseudodifferential Operators and Spectral Theory [Paperback]

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.I. Foundations of ?DO Theory.- ? 1. Oscillatory Integrals.- ? 2. Fourier Integral Operators (Preliminaries).- ? 3. The Algebra of Pseudodifferential Operators and Their Symbols.- ? 4. Change of Variables and Pseudodifferential Operators on Manifolds.- ? 5. Hypoellipticity and Ellipticity.- ? 6. Theorems on Boundedness and Compactness of Pseudodifferential Operators.- ? 7. The Sobolev Spaces.- ? 8. The Fredholm Property, Index and Spectrum.- II. Complex Powers of Elliptic Operators.- ? 9. Pseudodifferential Operators with Parameter. The Resolvent.- ? 10. Definition and Basic Properties of the Complex Powers of an Elliptic Operator.- ? 11. The StrlS)