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Published 2007 | Published
Book Section - Chapter Open

Orthogonal polynomials with exponentially decaying recursion coefficients

Simon, Barry ORCID icon
Others:
Molchanov, S. A.
Dawson, Donald Andrew
Jakšić, Vojkan
Vaĭnberg, B. R.
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Abstract

We review recent results on necessary and sufficient conditions for measures on R and ∂D to yield exponential decay of the recursion coefficients of the corresponding orthogonal polynomials. We include results on the relation of detailed asymptotics of the recursion coefficients to detailed analyticity of the measures. We present an analog of Carmona's formula for OPRL. A major role is played by the Szegö and Jost functions.

Additional Information

© 2007 Barry Simon. This is the final form of the paper. Dedicated to S. Molchanov on his 65th birthday. Submitted to the Proceedings of S. Molchanov's 65th Birthday Conference. This work is supported in part by NSF grant DMS-0140592.

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Published - Simon2007p9109Probability_And_Mathematical_Physics_A_Volume_In_Honor_Of_Stanislav_Molchanov.pdf

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Simon2007p9109Probability_And_Mathematical_Physics_A_Volume_In_Honor_Of_Stanislav_Molchanov.pdf

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