D. V. Gorbachev

Extremum problems for entire functions of exponential spherical type

We consider extremum problems for entire functions of exponential spherical type related to important extremum problems on the optimal point (the Chernykh point) in the sharp jackson inequality in the spaceL2(ℝn) and the connection between codes and designs on the torusTn.

Extremum Problem for Periodic Functions Supported in a Ball

AbstractWe consider the Turan n-dimensional extremum problem of finding the value of An(hBn) which is equal to the maximum zero Fourier coefficient

The Delsarte extremal problem for the Jacobi transform

\widehat f_0

Approximation in L 2 by partial integrals of the Fourier transform over the eigenfunctions of the Sturm–Liouville operator

of periodic functions f supported in the Euclidean ball hBn of radius h, having nonnegative Fourier coefficients, and satisfying the condition f(0)= 1. This problem originates from applications to number theory. The case of A1([−h,h]) was studied by S. B. Stechkin. For An(hBn we obtain an asymptotic series as h → 0 whose leading term is found by solving an n-dimensional extremum problem for entire functions of exponential type.

Approximation in L 2 by Partial Integrals of the Multidimensional Fourier Transform over the Eigenfunctions of the Sturm–Liouville Operator

In the space L2 on the real axis with hyperbolic weight, the sharp Jackson inequality with optimal argument is proved.

Some extremal problems for the Fourier transform on the hyperboloid

We give the solution of the Delsarte extremal problem for even entire functions of exponential type that are Jacobi transforms and prove the uniqueness of the extremal function. The quadrature Markov formula on the half-line with zeros of the modified Jacobi function are used.

An Extremum Problem for Periodic Functions with Small Support

We give a solution to Yudin’s extremum problem for algebraic polynomials related to codes and designs.

The sharp Jackson inequality in the spaceL p on the sphere

For approximations in the space L2(ℝ+) by partial integrals of the Fourier transform over the eigenfunctions of the Sturm–Liouville operator, we prove Jackson’s inequality with exact constant and optimal argument in the modulus of continuity. The optimality of the argument in the modulus of continuity is established using the Gauss quadrature formula on the half-line over the zeros of the eigenfunction of the Sturm–Liouville operator.