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Regular version of the site

Article

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

St Petersburg Mathematical Journal. 2015. Vol. 26. P. 867-879.
Gladkaya A., Виноградов О. Л.

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\geqslant m. Functions that have the smallest deviation from zero among the entire functions of type \sigma are constructed in the uniform and integral metrics.