Asymptotic Behavior of Nikolskii Constants for Polynomials on the Unit Circle

Eli Levin; Doron S. Lubinsky

doi:10.1007/s40315-015-0113-3

Asymptotic Behavior of Nikolskii Constants for Polynomials on the Unit Circle

Eli Levin, Doron S. Lubinsky

Mathematics discipline

Research output: Contribution to journal › Article › peer-review

Abstract

Let q>p>0, and consider the Nikolskii constants (Formula presented.) where the norm is with respect to normalized Lebesgue measure on the unit circle. We prove that (Formula presented.) where (Formula presented.), and the inf is taken over all entire functions f of exponential type at most π. We conjecture that the lim sup can be replaced by a limit.

Original language	English
Pages (from-to)	459-468
Number of pages	10
Journal	Computational Methods and Function Theory
Volume	15
Issue number	3
DOIs	https://doi.org/10.1007/s40315-015-0113-3
State	Published - 10 Sep 2015

Bibliographical note

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

Keywords

Nikolskii Inequalities
Paley–Wiener Spaces

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10.1007/s40315-015-0113-3

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Asymptotic Behavior of Nikolskii Constants for Polynomials on the Unit Circle

Abstract

Bibliographical note

Keywords

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