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Wiener-Hopf operators in higher dimensions: the Widom conjecture for piece-wise smooth domains

Published 6 Dec 2013 in math.SP, math-ph, and math.MP | (1312.1835v2)

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 the surfaces which are assumed to be piece-wise smooth. Such a two-term formula was conjectured by H. Widom in 1982, and proved by A. V Sobolev for smooth surfaces in 2009.

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