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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Asymptotic expansions of traces for certain convolution operators


Author: Raymond Roccaforte
Journal: Trans. Amer. Math. Soc. 285 (1984), 581-602
MSC: Primary 47B35; Secondary 45A05, 47B10
DOI: https://doi.org/10.1090/S0002-9947-1984-0752492-1
MathSciNet review: 752492
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Abstract: A version of Szegö's theorem in Euclidean space gives the first two terms of the asymptotics as $ \alpha \to \infty $ of the determinant of convolution operators on $ {L_2}(\alpha \,\Omega )$, where $ \Omega $ is a bounded subset of $ {{\mathbf{R}}^n}$ with smooth boundary. In this paper the more general problem of the asymptotics of traces of certain analytic functions of the operators is considered and the next term in the expansion is obtained.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0752492-1
Keywords: Szegö limit theorem, convolution operators, Wiener-Hopf operators, asymptotics of traces
Article copyright: © Copyright 1984 American Mathematical Society