Rational Approximation by Reproducing Kernel for Bergman Functions on Siegel Domains

ABSTRACT Based on recent developments of reproducing kernels in several complex variables, we study the kernel approximation for weighted Bergman functions on Siegel domains. To overcome the difficulties arising in Siegel domains, a new method is proposed in the proof of boundary vanishing property (BVP) at infinity by adopting the biholomorphic invariance property of weighted kernel functions. Once the BVP is verified, optimal parameters are selected and the corresponding orthogonal functions are constructed by induction according to the maximal selection principle.