Extreme eigenvalues of an integral operator

  • Alexander V. Sobolev

    University College London, UK
Extreme eigenvalues of an integral operator cover
Download PDF

A subscription is required to access this article.

Abstract

We study the family of compact operators , in , , where is the pseudo-differential operator with symbol , and both functions and are real-valued and decay at infinity. We assume that and attain their maximal values , only at and . We also assume that

with some functions , and , that are homogeneous of degree and respectively. The main result is the following asymptotic formula for the positive eigenvalues of the operator (arranged in descending order counting multiplicity) for fixed and :

where , and are the eigenvalues (arranged in ascending order counting multiplicity) of the model operator with symbol .

Cite this article

Alexander V. Sobolev, Extreme eigenvalues of an integral operator. J. Spectr. Theory 9 (2019), no. 1, pp. 227–241

DOI 10.4171/JST/246