The continuous wavelet transform in terms of generalized Kontorovich–Lebedev transform

In this paper, generalized continuous wavelet transform (generalized CWT) in terms of generalized Kontorovich–Lebedev transform (generalized KL-transform) has been introduced and various related results have been obtained. Estimate for the convolution operator associated to the generalized KL-transform has been deduced. Results related to generalized CWT, like Plancherel relation, Parseval’s relation and Reconstruction formula have been obtained.