Composition of wavelet transform 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 idea of Kontorovich-Lebedev transform (KL-transform). Estimates for family of KL-wavelet as well as KL-wavelet transform are obtained and Plancherel's relation for composition of KL-wavelet transform as well as WPT-transform is 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.