Uniform estimate for a segment function in terms of a polynomial strip

Dudov, S.; Sorina, E.

doi:10.1090/S1061-0022-2013-01262-3

Uniform estimate for a segment function in terms of a polynomial strip
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by S. I. Dudov and E. V. Sorina
Translated by: A. Plotkin

St. Petersburg Math. J. 24 (2013), 723-742

DOI: https://doi.org/10.1090/S1061-0022-2013-01262-3

Published electronically: July 24, 2013

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Abstract:

A problem about a uniform estimate for a continuous segment function in terms of a polynomial strip is considered. The problem reduces to a convex programming problem the target function of which is equal to the sum of the target functions for the inner and outer estimate of the same segment function via a polynomial strip. Convex analysis tools are used to obtain necessary and sufficient conditions for being a solution, and also uniqueness conditions in a form resembling the Chebyshov alternance.

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