Siegel-Szász extremal problem for a power weight

In the classical Siegel extremal problem one looks for the maximum value of an integral of a positive definite function with support in a Euclidean ball and fixed value at the origin. A Szász-type problem is similar, but the integral is taken with respect to a fixed radial measure. The multidimensional Siegel-Szász problem reduces to the one-dimensional problem on the real line with power weight. We present a general method for the solution of this problem, which reduces to the spectral analysis of the Dunkl integral convolution operator. The links with quadrature formulae for entire functions of exponential type and duality theory are discussed. Bibliography: 50 titles.