Wavelet transforms associated with the Kontorovich-Lebedev transform

摘要

The main objective of this paper is to study continuous wavelet transform (CWT) using the convolution theory of Kontorovich-Lebedev transform (KL-transform) and discuss some of its basic properties. Plancherel's as well as Parseval's relation and Reconstruction formula for CWT are obtained and some examples are also given. The discrete version of the wavelet transform associated with KL-transform is also given and reconstruction formula is derived.