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Entire functions that deviate least from zero in the uniform and the integral metrics with a weight


Authors: A. V. Gladkaya and O. L. Vinogradov
Translated by: O. L. Vinogradov
Original publication: Algebra i Analiz, tom 26 (2014), nomer 6.
Journal: St. Petersburg Math. J. 26 (2015), 867-879
MSC (2010): Primary 41A50; Secondary 30E10
DOI: https://doi.org/10.1090/spmj/1364
Published electronically: September 21, 2015
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Abstract | References | Similar Articles | Additional Information

Abstract: Results of Chebyshev and Bernstein about polynomials with the smallest deviation from zero in a weighted norm are extended to entire functions of exponential type. Suppose that a function $ \rho _m$ belongs to the Cartwright class, is of type $ m$, and is positive on the real axis. Let $ \sigma \geq m$. Functions that have the smallest deviation from zero among the entire functions of type $ \sigma $ are constructed in the uniform and integral metrics.


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Additional Information

A. V. Gladkaya
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskii pr. 28, Petrodvorets, 198504 St. Petersburg, Russia
Email: anna.v.gladkaya@gmail.com

O. L. Vinogradov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskii pr. 28, Petrodvorets, 198504 St. Petersburg, Russia
Email: olvin@math.spbu.ru

DOI: https://doi.org/10.1090/spmj/1364
Keywords: Entire functions, smallest deviation from zero, weighted spaces
Received by editor(s): August 1, 2013
Published electronically: September 21, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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