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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Scattering theory and polynomials orthogonal on the real line
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by J. S. Geronimo and K. M. Case PDF
Trans. Amer. Math. Soc. 258 (1980), 467-494 Request permission

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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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 258 (1980), 467-494
  • MSC: Primary 81F99; Secondary 30C10, 42C05
  • DOI: https://doi.org/10.1090/S0002-9947-1980-0558185-4
  • MathSciNet review: 558185