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Fourier Tauberian Theorems and Applications

✍ Scribed by Yu. Safarov

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
299 KB
Volume
185
Category
Article
ISSN
0022-1236

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✦ Synopsis

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 of 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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