Approximation of linear canonical wavelet transform on the generalized Sobolev spaces

The main objective of this paper is to study the linear canonical wavelet transform (LCWT) on generalized Sobolev space B-p,B- (xi,)(k) (A)(R) and generalized weighted space L-epsilon,L- (s,)(A) (p)(R). Its approximation properties and convergence of convolution for F-psi(A) in the space B-p,B- (xi,)(k) (A)(R) are also discussed. Based on these properties, we prove that the LCWT is linear continuous mapping on the spaces of F-p,F- (A)* and U-p,U- (k)(A). The composition of LCWTs is defined and studied some results related to it. Moreover, the boundedness results of LCWT as well as composition of LCWTs on the space H-epsilon,H- (As)(R) are studied.