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Pseudo-differential operators with discontinuous symbols : Widom's conjecture / A.V. Sobolev.

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Author/Creator:
Sobolev, A. V. (Aleksandr Vladimirovich)
Language:
English.
Publication date:
2013
Publication:
Providence, Rhode Island : American Mathematical Society, 2013.
Format:
  • Book
  • v, 104 pages ; 25 cm.
Note:
"March 2013, Volume 222, Number 1043 (second of 5 numbers)."
Bibliography:
Includes bibliographical references (pages 103-104) and index.
Contents:
  • Introduction
  • Main result
  • Estimates for PDO's with smooth symbols
  • Trace-class estimates for operators with non-smooth symbols
  • Further trace-class estimates for operators with non-smooth symbols
  • A Hilbert-Schmidt 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 trace-class formula
  • Appendix 4: invariance with respect to the affine change of variables.
Series:
Memoirs of the American Mathematical Society, 0065-9266 ; no. 1043
Memoirs of the American Mathematical Society ; no. 1043.
Subjects:
ISBN:
9780821884874
0821884875

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