Multiresolution in the Bergman space

Abstract. In this paper we introduce a new example of sampling set for the Bergman space which can be connected to the Blaschke group operation. Using this set we will generate a multiresolution analysis in the Bergman space and we present properties of the projection operator on the resolution levels. The construction is an analogy with the multiresolution generated by the discrete affine wavelets in the space of the square integrable functions on the real line, and in fact is the discretization of the continuous voice transform generated by a representation of the Blaschke group over the Bergman space.