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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Spectral properties of orthogonal polynomials on unbounded sets


Author: T. S. Chihara
Journal: Trans. Amer. Math. Soc. 270 (1982), 623-639
MSC: Primary 42C05
DOI: https://doi.org/10.1090/S0002-9947-1982-0645334-4
MathSciNet review: 645334
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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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DOI: https://doi.org/10.1090/S0002-9947-1982-0645334-4
Article copyright: © Copyright 1982 American Mathematical Society