An unusual eigenvalue problem

TL;DR

This paper investigates a unique eigenvalue problem linked to the stability analysis of a self-similar attractor in the sigma model, introducing a specialized continued fraction method for eigenvalue determination.

Contribution

It presents a novel eigenvalue problem in spectral theory and develops a continued fraction approach to solve it, addressing its unusual characteristics.

Findings

Eigenvalues determined using the continued fraction method

The eigenvalue problem's spectral properties are characterized

New techniques for solving atypical eigenvalue problems

Abstract

We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral theory of linear operators and requires special methods to solve it. One of such methods based on continued fractions is presented in detail and applied to determine the eigenvalues.