Spectral measure corresponding to orthogonal polynomials defined by three-term recurrence relation

Abstract

Suppose that a Borel measure with infinite support is given. Then it is known that the orthogonal polynomial system exists. Conversely, if the polynomial systems satisfying the three-term recurrence relation are given, then the measure of orthogonality exists. In this thesis, we will discuss the relationship between the coefficients of the three-term recurrence relation and the nature of the spectral measure, support, absolute continuity. In this thesis, the properties of the spectral measure is obtained by the tools of functional analysis, operator theory, and perturbation theory.