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).
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Sobolev, A.V. Wiener–Hopf Operators in Higher Dimensions: The Widom Conjecture for Piece-Wise Smooth Domains. Integr. Equ. Oper. Theory 81, 435–449 (2015). https://doi.org/10.1007/s00020-014-2185-2
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DOI: https://doi.org/10.1007/s00020-014-2185-2