Bergman kernel asymptotics for generalized Fock spaces

Letm(t)dt be a positive measure onR ⁺. We investigate the relations among the growth ofm, the growth of its moment sequence {y_n}, the growth of its Bergman kernel functionk x=Σγ{_n/^-1}x ⁿ, and the growth of the kernel function associated to the measureK(t) ⁻¹m(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 ⁻¹. Supported in part by a grant from the National Science Foundation.