Yu.S. Volkov. Euler polynomials in the problem of extremal functional interpolation in the mean ... P. 83-97

The problem of extremal functional interpolation in the mean, first studied by Yu. N. Subbotin, is considered. Representations of the extremal functions solving this problem in terms of Euler polynomials are found, and their properties are studied. This made it possible to calculate the values of the extremal interpolation constants in terms of easily computable values of the Euler polynomials at certain points and sometimes Favard constants. The compatibility of the constants of extremal functional interpolation in the mean as the value of the averaging interval tends to zero with the constants of extremal functional interpolation is demonstrated.

Keywords: Euler polynomials, Favard constants, interpolation in the mean

Received June 5, 2020

Revised November 1, 2020

Accepted November 9, 2020

Funding Agency: This work was supported by the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (state contract no. 0314-2016-0013), and partially by the Russian Foundation for Basic Research and the German Research Foundation (project no. 19-51-12008).

Yuriy Stepanovich Volkov, Dr. Phys.-Math. Sci., Prof., Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090 Russia, e-mail: volkov@math.nsc.ru

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Cite this article as: Yu.S. Volkov. Euler polynomials in the problem of extremal functional interpolation in the mean, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2020, vol. 26, no. 4, pp. 83–97.