Biortogon dan sifat penjanaan semula

Abstract

Integral operators involving the Szego, the Bergman and the Cauchy kernels are known to have reproducing property, i.e. all of them reproduce holomorphic functions. Both the Szego and the Bergman kernels have series representations in terms of orthonormal basis. In this paper we derive the Cauchy kernel by means of biorthoganality. The ideas involved are then applied to constuct a non-Hermitian kernel admitting reproducing property of the space associated with the Bergman kernel.