| Abstract: | We establish a relationship between the Logan problem for functions whose Fourier transform is supported in a centrally symmetric convex closed subset of ℝ m and whose mean value on ℝ m is nonnegative and the Chernykh problem on the optimal point for the Jackson inequality inL 2(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. Both problems are solved exactly in several cases. Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp. 336–350, September, 1999. |
