Generalized Jacobi operators in Krein spaces

TL;DR

This paper studies a class of self-adjoint generalized Jacobi operators in Krein spaces, describing their spectral properties and applying these results to convergence of Padé approximants.

Contribution

It introduces a special class of generalized Jacobi operators in Krein spaces and analyzes their spectral properties, especially for periodic cases, with applications to Padé approximation convergence.

Findings

Spectral properties of generalized Jacobi operators are characterized.

Resolvent set described via recurrence relations.

Convergence results for Padé approximants are established.

Abstract

A special class of generalized Jacobi operators which are self-adjoint in Krein spaces is presented. A description of the resolvent set of such operators in terms of solutions of the corresponding recurrence relations is given. In particular, special attention is paid to the periodic generalized Jacobi operators. Finally, the spectral properties of generalized Jacobi operators are applied to prove convergence results for Pad\'e approximants.