## 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 Ingen eksempelvisning - 2001 |

### Almindelige termer og sætninger

adjoint am(x amplitude anti-Wick symbol arbitrary assume asymptotic behaviour asymptotic expansion asymptotic formula Au(x bicharacteristic Cauchy problem closed manifold compact set complex powers compute condition conic neighbourhood consider constants construct converges coordinates Corollary corresponding defined Definition denote depend diffeomorphism differential operator eigenvalues elliptic differential operator elliptic operator equal equation equivalent Exercise exists expression finite following estimate holds Fourier transform Hilbert space holomorphic homogeneous of degree Hormander Hs(K Hs(M hypoelliptic implies Laplace operator Lemma multi-indices Note obtain obvious open set oscillatory integral parametrix phase function polar decomposition polynomial positive homogeneous principal symbol proof of Theorem properly supported TDO Proposition Pseudodifferential Operators S(IR satisfies scalar product self-adjoint Show sing supp smooth kernel smooth positive density Sobolev spaces solution statement subset T-symbol theory topology trace class vector Weyl symbol WF(u

### Populære passager

Side 275 - VK [1973] On the heat equation and the index theorem. Invent. Math. 19, 279-330.

Side 281 - On local solvability of linear partial differential equations. Part I: Necessary conditions.

Side 276 - VP, Nikolskii, SM [1] 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.

Side 276 - Bony [Seminaire Goulaouic-Schwartz 1975/1976: Equations aux Derivees Partielles et Analyse Fonctionnelle, Exp. No.

### Henvisninger til denne bog

Nonlinear Functional Analysis and Its Applications: Part 2 B: Nonlinear ... E. Zeidler Ingen eksempelvisning - 1989 |

Elliptic Problems in Domains with Piecewise Smooth Boundaries S. A. Nazarov,B. A. Plamenevskiĭ Begrænset visning - 1994 |