傅立叶-陶伯定理及其应用
Fourier Tauberian Theorems and Applications
摘要：
本文的主要目的是给出单调函数的傅立叶-陶伯定理的一般形式。这个结果，加上Berezin不等式，使我们得到了Dirichlet Laplacian的计数函数的Li-Yau估计的一个改进版本，这意味着Li-Yau估计本身，同时，也得到了用变分方法得到的渐近结果.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
