Sampling in Weighted Lp Spaces of Entire Functions in Cn and Estimates of the Bergman Kernel

The necessary density condition in C known for sampling and interpolation in the Lp space of entire functions with a subharmonic weight is extended to the case of a 2-homogeneous, plurisubharmonic weight function in C. The method is by estimating the eigenvalues of a certain Toeplitz concentration operator, using asymptotic estimates for the Bergman kernel of independent interest.