Fourier Tauberian Theorems and Applications

Y Safarov

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Fourier Tauberian Theorems and Applications

Y Safarov

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Abstract

The main aim of the paper is to present a general version of the Fourier Tauberian theorem for monotone functions. This result, together with Berezin's inequality, allows us to obtain a refined version the Li-Yau estimate for the counting function of the Dirichlet Laplacian which implies the Li-Yau estimate itself and, at the same time, the asymptotic results obtained by the variational method.

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BibTeX RIS

Y Safarov. 2000-03-02. Fourier Tauberian Theorems and Applications. https://arxiv.org/abs/math/0003014

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