Spectral properties of orthogonal polynomials on unbounded sets

Chihara, T. S.

doi:10.1090/S0002-9947-1982-0645334-4

Spectral properties of orthogonal polynomials on unbounded sets
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Trans. Amer. Math. Soc. 270 (1982), 623-639 Request permission

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 $\sigma$? If $\sigma$ is finite, when will there be at most finitely many spectral points smaller than $\sigma$; and when will the distribution function be continuous at $\sigma$?

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