Orthogonal polynomials with exponentially decaying recursion coefficients

Details Orthogonal polynomials with exponentially decaying recursion coefficients Orthogonal polynomials with exponentially decaying recursion coefficients

2006-03-03

arxiv.org/abs/math/0603099v1

Mathematics

Spectral Theory

13 pages

Scientific paper

We review recent results on necessary and sufficient conditions for measures on $\mathbb{R}$ and $\partial\mathbb{D}$ 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 Szego and Jost functions.

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