Bergman kernel asymptotics for generalized Fock spaces

Letm(t)dt be a positive measure onR^sup +^. We investigate the relations among the growth ofm, the growth of its moment sequence {y^sub n^}, the growth of its Bergman kernel functionk x=Σγ{^sub n^/^sup -1^}x^sup n^, and the growth of the kernel function associated to the measureK(t)^sup -1^m(t) dt. For a large class of measures, we find that these quantities satisfy asymptotic relations similar to the simple exact relations which hold in the model casem(t)=e^sup -1^.[PUBLICATION ABSTRACT]