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

Gladkaya, A.; Vinogradov, O.

doi:10.1090/spmj/1364

Entire functions that deviate least from zero in the uniform and the integral metrics with a weight
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by A. V. Gladkaya and O. L. Vinogradov
Translated by: O. L. Vinogradov

St. Petersburg Math. J. 26 (2015), 867-879

DOI: https://doi.org/10.1090/spmj/1364

Published electronically: September 21, 2015

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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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