ANALYTIC FUNCTIONS OF THE CLASSES L2 AND I2 AND THEIR KERNEL FUNCTIONS

摘要

In fact, using R. Nevanlinna's investigation [13], concerning the dimension of the Hilbert space formed by the functions of the class L2 (D), with respect to the metric (2.9), we prove, by using standard methods, that two domains possess the same kernel function, if and only if they possess the same Green function. Our results are complete for the case of finitely-connected domains, because an isolated point is a null-set. The situation is different in the case of infinitely connected domains.