Orthogonal polynomials with exponentially decaying recursion coefficients

2006/03/03 by Barry Simon, Simon, Barry · 2 citations
Computer Science · Mathematics · #05E35 #30D30 #47B36 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms #Spectral Theory (math.SP) #math.CA #math.SP #msc:05E35 #msc:30D30 #msc:47B36

paper · pdf · doi:10.48550/arxiv.math/0603099

13 pages

arxiv created 2006/03/03 · openalex publication_date 2006/03/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review recent results on necessary and sufficient conditions for measures on ℝ and ∂\mathbbD 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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