Sobolev, AV;
(2015)
Wiener–Hopf Operators in Higher Dimensions: The Widom Conjecture for Piece-Wise Smooth Domains.
Integral Equations and Operator Theory
, 81
(3)
435 - 449.
10.1007/s00020-014-2185-2.
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Abstract
We prove a two-term quasi-classical trace asymptotic formula for the functions of multi-dimensional Wiener–Hopf operators with discontinuous symbols. The discontinuities occur on surfaces which are assumed to be piece-wise smooth. Such a two-term formula was conjectured by H. Widom (On a Class of Integral Operators with Discontinuous Symbol, Toeplitz centennial (Tel Aviv, 1981), pp. 477–500. Operator Theory: Advances and Applications, vol. 4. Birkhäuser, Basel, 1982), and proved by A. V. Sobolev for smooth surfaces in 2009 (Mem. AMS 222(1043), 2013).
| Type: | Article |
|---|---|
| Title: | Wiener–Hopf Operators in Higher Dimensions: The Widom Conjecture for Piece-Wise Smooth Domains |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00020-014-2185-2 |
| Publisher version: | http://dx.doi.org/10.1007/s00020-014-2185-2 |
| Additional information: | This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited. |
| Keywords: | Primary 47G30, 35S05, Secondary 45M05, 47B10, 47B35, Wiener–Hopf operators, Pseudo-differential operators with discontinuous symbols, Quasi-classical asymptotics |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1460988 |
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