Widow factors for the Hilbert norm

Date
2015
Authors
Alpan, G.
Goncharov, A.
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Source Title
Institute of Mathematıcs Polish Academy of Sciences
Print ISSN
0239-7269
Electronic ISSN
1732-8985
Publisher
Polska Akademia Nauk
Volume
107
Issue
Pages
11 - 18
Language
English
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Abstract

Given a probability measure µ with non-polar compact support K, we define the n-th Widom factor W2n(µ) as the ratio of the Hilbert norm of the monic n-th orthogonal polynomial and the n-th power of the logarithmic capacity of K. If µ is regular in the Stahl–Totik sense then the sequence (W2n(µ))∞n=0 has subexponential growth. For measures from the Szegő class on [−1, 1] this sequence converges to some proper value. We calculate the corresponding limit for the measure that generates the Jacobi polynomials, analyze the behavior of the corresponding limit as a function of the parameters and review some other examples of measures when Widom factors can be evaluated.

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