Extremal Functions and Calderón's Reproducing Formula for the Laguerre-Bessel Two-Wavelet Transform

The main purpose of this paper is to study the wavelet transform associated with the Laguerre-Bessel transform and to provide an integral representation of the extremal function related to this transform. We then introduce the notion of a Laguerre-Bessel two-wavelet and present generalized versions of Parseval's, inversion and Calder\'on's type reproducing formulas related to this transform.