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The Heat Expansion for Systems of Integral Equations

  • Harold Widom
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 35)

Abstract

In this paper we derive an analogue for integral operators of the well-known heat expansion for the Laplacian or other operators of positive order. Previous work established a partial expansion of n + 1 terms for a single integral operator in n dimensions. This is here extended to systems of operators.

Keywords

Pseudodifferential Operator Pseudo Differential Operator Numerical Range Positive Order Symbol Class 
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References

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    S. Birman and M.Z. Solomjak, Asymptotic behavior of the spectrum of weakly polar integral operators, Math. USSR-Izvestija, 4 (1970) 1151–1168.CrossRefGoogle Scholar
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    G.I. Eskin, Boundary value problems for elliptic pseudo-differential equations, Amer. Math. Soc. Transi, of Math. Monographs, 52 (1981).Google Scholar
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    G. Grubb, The heat equation associated with a pseudo-differential boundary problem, Copenhagen Univ. Math. Inst. (preprint), 2 (1982).Google Scholar
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    E.C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford, 1948.Google Scholar
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    H. Widom, Asymptotic expansions for pseudo-differential operators on bounded domains, Springer Lecture Notes in Math, 1152 (1986).Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1988

Authors and Affiliations

  • Harold Widom
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaSanta CruzUSA

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