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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Scattering theory and polynomials orthogonal on the real line


Authors: J. S. Geronimo and K. M. Case
Journal: Trans. Amer. Math. Soc. 258 (1980), 467-494
MSC: Primary 81F99; Secondary 30C10, 42C05
MathSciNet review: 558185
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Abstract: The techniques of scattering theory are used to study polynomials orthogonal on a segment of the real line. Instead of applying these techniques to the usual three-term recurrence formula, we derive a set of two two-term recurrence formulas satisfied by these polynomials. One of the advantages of these new recurrence formulas is that the Jost function is related, in the limit as $ n\, \to \,\infty $, to the solution of one of the recurrence formulas with the boundary conditions given at $ n\, = \,0$. In this paper we investigate the properties of the Jost function and the spectral function assuming the coefficients in the recurrence formulas converge at a particular rate.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0558185-4
PII: S 0002-9947(1980)0558185-4
Article copyright: © Copyright 1980 American Mathematical Society