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Two related extremal problems for entire functions of several variables. (English. Russian original) Zbl 0976.41015
Math. Notes 66, No. 3, 271-282 (1999); translation from Mat. Zametki 66, No. 3, 336-350 (1999).
From the abstract: The author establishes a relationship between the Logan problem for functions whose Fourier transform is supported in a centrally symmetric convex closed subset of \(\mathbb R^m\) and whose mean value on \(\mathbb R^m\) is nonnegative and the Chernykh problem on the optimal point for the Jackson inequality in \(L_2(\mathbb R^m)\), which relates the best approximation of a function by the class of entire functions of exponential type to the first modulus of continuity.

MSC:
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
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