On a Tauberian theorem with the remainder term and its application to the Weyl law

The purpose of this paper is twofold. First, we prove a generalization of the classical Tauberian theorem for the Laplace transform obtained by A. M. Subhankulov which gives an optimal bound for the remainder term. Second, we apply the Subhankulov theorem to a suitably transformed trace formula in t...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 401; no. 1; pp. 317 - 335
Main Authors Smajlović, Lejla, Šćeta, Lamija
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.05.2013
Subjects
Rank one symmetric spaces
Tauberian theorem
The Weyl law
The Weyl law
Tauberian theorem
Rank one symmetric spaces
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Summary:The purpose of this paper is twofold. First, we prove a generalization of the classical Tauberian theorem for the Laplace transform obtained by A. M. Subhankulov which gives an optimal bound for the remainder term. Second, we apply the Subhankulov theorem to a suitably transformed trace formula in the setting of symmetric spaces of real rank one and obtain an improved bound for the remainder term in the Weyl law. Our analysis is valid assuming an order of growth of the logarithmic derivative of the scattering determinant along imaginary axes.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.09.039