Simon, Barry (2007) Orthogonal polynomials with exponentially decaying recursion coefficients. In: Probability and mathematical physics : a volume in honor of Stanislav Molchanov. CRM Proceedings & Lecture Notes (42). American Mathematical Society , Providence, RI, pp. 453-463. ISBN 9780821840894 http://resolver.caltech.edu/CaltechAUTHORS:20110107-081647098
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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.
|Item Type:||Book Section|
|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.|
|Subject Keywords:||Spectral Theory (math.SP); Classical Analysis and ODEs (math.CA)|
|Classification Code:||2000 Mathematics Subject Classification: Primary 42C05, 42C25, 34L05; Secondary 33C45, 33C47, 39A10|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||25 Jan 2011 18:20|
|Last Modified:||26 Dec 2012 12:49|
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