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Factorization of second order difference equations and its application to orthogonal polynomials

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1329)

Abstract

It is shown that a second order recurrence expression with coefficients having bounded variation, written as a second degree polynomial of the forward shift operator, can be factored as the product of two first order expressions. This result is used to obtain asymptotics over the complex plane for a class of polynomials orthonormal over the real line.

This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-8601184 (first author) and DMS-8419525 (second author), and by the PSC-CUNY Research Award Program of the City University of New York under Grant No. 6-66429 (first author).

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References

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© 1988 Springer-Verlag

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Máté, A., Nevai, P. (1988). Factorization of second order difference equations and its application to orthogonal polynomials. In: Alfaro, M., Dehesa, J.S., Marcellan, F.J., Rubio de Francia, J.L., Vinuesa, J. (eds) Orthogonal Polynomials and their Applications. Lecture Notes in Mathematics, vol 1329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083357

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  • DOI: https://doi.org/10.1007/BFb0083357

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19489-7

  • Online ISBN: 978-3-540-39295-8

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