Optimal interpolating spaces generated by the Abel-Jacobi elliptic functions

The classical Abel-Jacobi elliptic functions have been extensively

used in the Approximation Theory and, in particular, in the Optimal Recovery problems. Such functions posses a variety of very attractive properties, being much more  exible and versatile in comparison to the circular functions. I will consider several examples of linear interpolating spaces generated by such functions. A notion of an optimal interpolating space will be discussed, drawing on some applications in statistical problems of random data approximation. Conditions will be presented under which the interpolating spaces generated by the Abel-Jacobi elliptic functions contain constants and are optimal, in the case of equidistant interpolating design. I will also mention some open problems related to a possible extension of these results to the more general class of automorphic functions.