Trace formulas for a class of Jacobi operators

TL;DR

This paper derives trace formulas and analyzes the asymptotic behavior of Green's functions for a specific class of Jacobi operators generated by measures supported on multiple intervals and symmetric points outside their convex hull.

Contribution

It introduces new trace formulas and asymptotic analysis for Jacobi operators with measures supported on multiple intervals and symmetric points outside their convex hull.

Findings

Asymptotic behavior of the diagonal Green's function is characterized.

Trace formulas for sequences of coefficients are established.

The class of operators includes measures supported on multiple intervals and symmetric points.

Abstract

In this paper we study a class of Jacobi operators, such that each operator is generated by the unit Borel measure with a support consisting of a finite number of intervals on the real line R and a finite number of points in C, located outside the convex hull of the intervals and symmetrically with respect to R. In such a class of operators we have obtained the asymptotic behavior of the diagonal Green's function and trace formulas for sequences of coefficients corresponding to a given operator. Bibliography: 34 titles.