分数阶微分算子特征值的渐近性
泛函分析
2020-02-06 v3
摘要
本文研究一个二阶多维分数阶微分算子。我们考虑主项由一致椭圆算子表示、末项为 Kipriyanov 分数阶微分算子的情形。我们根据此类算子的预解式是否属于 Schatten-von Neumann 类对其进行分类，并给出根函数系完备性的充分条件。最后，我们得到一个渐近公式。
引用
@article{arxiv.1804.10840,
title = {Asymptotics of Eigenvalues for Differential Operators of Fractional Order},
author = {M. V. Kukushkin},
journal= {arXiv preprint arXiv:1804.10840},
year = {2020}
}
备注
The report devoted to the results of this work took place 06.12.2017 at the seminar of Department of mathematical physics St. Petersburg state University, Saint Petersburg branch of V.A. Steklov Mathematical Institute of the Russian Academy of science, Russia, Saint Petersburg