Pseudodifferential Operators and Spectral TheoryI 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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Pseudodifferential Operators and Spectral Theory M. A. Shubin,S. I. Andersson No preview available - 2001 |
Common terms and phrases
a₁ A₂ anti-Wick symbol arbitrary assume asymptotic behaviour B₁ bicharacteristic C₁ Cauchy problem closed manifold compact set condition conic neighbourhood continuous converges coordinates Corollary đặ đč defined Definition denote diffeomorphism differential operator đŋ E₁ E₂ eigenvalues elliptic differential operator elliptic operator equation Exercise exists Fourier transform Fredholm H₁ H₂ Hilbert space holomorphic Hörmander hypoelliptic K₁ K₂ kernel L₁ Laplace operator Lemma linear multi-indices norm Note obtain obvious open set orthonormal oscillatory integral parameter parametrix phase function polynomial principal symbol proof of Theorem properly supported YDO Proposition prove pseudodifferential operators R₁ S(IR satisfies scalar product self-adjoint Show smooth Sobolev spaces space subspace supp t-symbol t₁ topology trace class vector verify Weyl symbol X₁
Popular passages
Page 275 - VK [1973] On the heat equation and the index theorem. Invent. Math. 19, 279-330.
Page 281 - On local solvability of linear partial differential equations. Part I: Necessary conditions.
Page 276 - VP, Nikolskii, SM [1] Integral representations of functions and imbedding theorems. Vol. I. Translated from the Russian.
Page 276 - Tenth Mathematical School (Summer School, Kaciveli/Nalchik, 1972), pp. 5-189. Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev 1974.
Page 278 - On necessary conditions for the solvability of pseudodifferential equations of principal type, Trudy Moskov. Mat. Obsc. 24 (1971), 29-41 =Trans.
Page 276 - Bony [Seminaire Goulaouic-Schwartz 1975/1976: Equations aux Derivees Partielles et Analyse Fonctionnelle, Exp. No.