Spectral properties of orthogonal polynomials on unbounded sets

Abstract

We consider orthogonal polynomials when the three term recurrence formula for the monic polynomials has unbounded coefficients. We obtain information relative to three questions: Under what conditions on the coefficients will the derived set of the spectrum have a finite infimum σ \sigma ? If σ \sigma is finite, when will there be at most finitely many spectral points smaller than σ \sigma ; and when will the distribution function be continuous at σ \sigma ?