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

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arxiv 1312.1835 v2 pith:YN4XRNRV submitted 2013-12-06 math.SP math-phmath.MP

A. V. Sobolev This is my paper · ORCID
classification math.SPmath-phmath.MP
keywords smoothformulaoperatorspiece-wisesurfacestwo-termwidomwiener-hopf
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Tensor factorization and explicit spectral bounds for product-box concentration operators

    math.FA 2026-07 accept novelty 6.0 of 10

    Finite box unions admit a fully explicit all-parameter plunge-count bound; cubes have an Omega((log c)^d) lower block and fixed-order trace asymptotics, proved via exact tensor structure.

  2. An independent proof of the plunge-region conjecture for time-frequency localization operators in dimension one

    math.FA 2026-07 accept novelty 5.0 of 10

    In one dimension, the plunge eigenvalue count of a time–frequency localization operator with finite-boundary windows is O(ln(1/ε) ln(c/ln(1/ε))).

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