Pseudodifferential Operators and Spectral Theory
Springer Science & Business Media, 3. jul. 2001 - 288 sider
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.
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arbitrary assume asymptotic Banach space belongs called clear clearly closed compact set complex compute condition consider constants construct continuous converges coordinates Corollary corresponding defined Definition denote depend derivatives differential operator eigenvalues elliptic equal equation equivalent estimate Exercise exists expression extended fact fixed follows formula Fourier given gives hence holds homogeneous homogeneous functions implies independent integral introduce kernel Lemma linear manifold neighbourhood norm Note obtain obvious operator parameter parametrix particular phase function positive Problem projection Proof proof of Theorem properly supported Proposition prove relation remains Remark respect satisfies self-adjoint sense Show side smooth solution space spectral statement suffices supp symbol Theorem theory topology transformation values vector verify Weyl symbol write
Side 275 - VK  On the heat equation and the index theorem. Invent. Math. 19, 279-330.
Side 276 - VP, Nikolskii, SM  Integral representations of functions and imbedding theorems. Vol. I. Translated from the Russian.
Side 276 - Tenth Mathematical School (Summer School, Kaciveli/Nalchik, 1972), pp. 5-189. Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev 1974.
Side 278 - On necessary conditions for the solvability of pseudodifferential equations of principal type, Trudy Moskov. Mat. Obsc. 24 (1971), 29-41 =Trans.
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