Discrete orthogonality of the analytic wavelets in the Hardy space of the upper half plane

Abstract

We will prove that the analytic orthogonal wavelet-system, which was introduced by Feichtinger and Pap in [Hyperbolic wavelets and multiresolution in the Hardy space of the upper half plane, in Blaschke Products and Their Applications: Fields Institute Communications, Vol. 65 (Springer, New York, 2013), pp. 193–208] is discrete orthogonal too. We will discuss the discrete orthogonality and the properties of the reproducing kernel functions of the introduced wavelet-spaces.