Composition of wavelet transforms and wave packet transform involving Kontorovich-Lebedev transform

Abstract

The main objective of this paper is to study the composition of continuous Kontorovich-Lebedev wavelet transform (KL-wavelet transform) and wave packet transform (WPT) based on the Kontorovich-Lebedev transform (KL-transform). Estimates for KL-wavelet and KL-wavelet transform are obtained, and Plancherel?s relation for composition of KL-wavelet transform and WPT-transform are derived. Reconstruction formula for WPT associated to KL-transform is also deduced and at the end Calderon?s formula related to KL-transform using its convolution property is obtained.