Pseudodifferential operators with discontinuous symbols : Widom's conjecture
 Responsibility
 A.V. Sobolev.
 Publication
 Providence, Rhode Island : American Mathematical Society, 2013.
 Physical description
 v, 104 pages ; 25 cm.
 Series
 Memoirs of the American Mathematical Society ; no. 1043.
Access
Available online
Science Library (Li and Ma)
Serials
Call number  Status 

Shelved by Series title NO.1043  Unknown 
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Creators/Contributors
 Author/Creator
 Sobolev, A. V. (Aleksandr Vladimirovich)
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 103104) and index.
 Contents

 Introduction Main result Estimates for PDO's with smooth symbols Traceclass estimates for operators with nonsmooth symbols} Further traceclass estimates for operators with nonsmooth symbols A HilbertSchmidt class estimate Localisation Model problem in dimension one Partitions of unity, and a reduction to the flat boundary Asymptotics of the trace (9.1) Proof of Theorem 2.9 Closing the asymptotics: Proof of Theorems 2.3 and 2.4 Appendix 1: A lemma by H. Widom Appendix 2: Change of variables Appendix 3: A traceclass formula Appendix 4: Invariance with respect to the affine change of variables Bibliography.
 (source: Nielsen Book Data)9780821884874 20160612
 Publisher's Summary
 Relying on the known twoterm quasiclassical asymptotic formula for the trace of the function f(A) of a WienerHopf type operator A in dimension one, in 1982 H. Widom conjectured a multidimensional generalisation of that formula for a pseudodifferential operator A with a symbol a(x, ?) having jump discontinuities in both variables. In 1990 he proved the conjecture for the special case when the jump in any of the two variables occurs on a hyperplane. The present paper provides a proof of Widom's Conjecture under the assumption that the symbol has jumps in both variables on arbitrary smooth bounded surfaces.
(source: Nielsen Book Data)9780821884874 20160612
Subjects
Bibliographic information
 Publication date
 2013
 Series
 Memoirs of the American Mathematical Society, 00659266 ; no. 1043
 Note
 "March 2013, Volume 222, Number 1043 (second of 5 numbers)."
 ISBN
 9780821884874 (alk. paper)
 0821884875 (alk. paper)