Asymptotics of Eigenvalues for Differential Operators of Fractional Order
Abstract
In this paper we deal with a second order multidimensional fractional differential operator. We consider a case where the leading term represented by the uniformly elliptic operator and the final term is the Kipriyanov operator of fractional differentiation. We conduct classification of such a type of operators by belonging of their resolvent to the Schatten-von Neumann class and formulate the sufficient condition for completeness of the root functions system. Finally we obtain an asymptotic formula.
Keywords
Cite
@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}
}
Comments
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