A family of anisotropic integral operators and behavior of its maximal eigenvalue
Boris S. Mityagin
Ohio State University, Columbus, USAAlexander V. Sobolev
University College London, UK
![A family of anisotropic integral operators and behavior of its maximal eigenvalue cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jst-volume-1-issue-4.png&w=3840&q=90)
Abstract
We study the family of compact integral operators in with the kernel
depending on the parameter , where is a symmetric non-\hspace{0pt}negative homogeneous function of degree . The main result is the following asymptotic formula for the maximal eigenvalue of :
where is the lowest eigenvalue of the operator . A central role in the proof is played by the fact that is positivity improving. The case has been studied earlier in the literature as a simplified model of high-temperature superconductivity.
Cite this article
Boris S. Mityagin, Alexander V. Sobolev, A family of anisotropic integral operators and behavior of its maximal eigenvalue. J. Spectr. Theory 1 (2011), no. 4, pp. 443–460
DOI 10.4171/JST/19