Sharp lower bounds for the Widom factors on the real line

Gökalp Alpan; Maxim Zinchenko

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arXiv · 1907.12492

Sharp lower bounds for the Widom factors on the real line

Gökalp Alpan·Maxim Zinchenko

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Abstract

We derive lower bounds for the $L^p(\mu)$ norms of monic extremal polynomials with respect to compactly supported probability measures $\mu$. We obtain a sharp universal lower bound for all $0<p<\infty$ and all measures in the Szeg\H{o} class and an improved lower bound on $L^2(\mu)$ norm for several classes of orthogonal polynomials including Jacobi polynomials, isospectral torus of a finite gap set and orthogonal polynomials with respect to the equilibrium measure of an arbitrary non-polar compact subset of $\mathbb{R}$.

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BibTeX RIS

Gökalp Alpan, Maxim Zinchenko. 2019-07-29. Sharp lower bounds for the Widom factors on the real line. https://arxiv.org/abs/1907.12492

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