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 , to the solution of one of the recurrence formulas with the boundary conditions given at . 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:
https://doi.org/10.1090/S0002-9947-1980-0558185-4

Article copyright:
© Copyright 1980
American Mathematical Society