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June 1995 On an Extension of the Ikehara Tauberian Theorem II
Junichi ARAMAKI
Tokyo J. Math. 18(1): 91-110 (June 1995). DOI: 10.3836/tjm/1270043611

Abstract

We consider a positively definite self-adjoint operator $P$ on a separable Hilbert space $H$ which has a compact resolvent. Then a specific example of the Ikehara Tauberian theorem is extended to the case where the zeta function of $P$ only has simple poles. In such circumstances, we can obtain the asymptotic behavior of the counting function of eigenvalues with remainder terms. And we have their applications to some partial differential operators.

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Junichi ARAMAKI. "On an Extension of the Ikehara Tauberian Theorem II." Tokyo J. Math. 18 (1) 91 - 110, June 1995. https://doi.org/10.3836/tjm/1270043611

Information

Published: June 1995
First available in Project Euclid: 31 March 2010

zbMATH: 0832.47020
MathSciNet: MR1334708
Digital Object Identifier: 10.3836/tjm/1270043611

Rights: Copyright © 1995 Publication Committee for the Tokyo Journal of Mathematics

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Vol.18 • No. 1 • June 1995
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