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Volume estimates and spectral asymptotics for a class of pseudo-differential operators

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Abstract

Two asymptotic expansions, known as the heat and Szegö expansions, are studied for a class of operators defined on \(L^2(\Omega )\) where \(\Omega \) is a compact region in Euclidean space with smooth boundary. Pseudo-differential operator methods are combined with a version of a theorem originally due to H. Weyl on the volume of certain tubular neighborhoods to obtain significant new information about the higher order terms in the expansions.

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  1. Los Altos, CA, USA

    Raymond Roccaforte

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  1. Raymond Roccaforte
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Correspondence to Raymond Roccaforte.

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Roccaforte, R. Volume estimates and spectral asymptotics for a class of pseudo-differential operators. J. Pseudo-Differ. Oper. Appl. 4, 25–43 (2013). https://doi.org/10.1007/s11868-012-0058-5

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  • DOI: https://doi.org/10.1007/s11868-012-0058-5

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