Approximation of linear canonical wavelet transform on the generalized Sobolev spaces

  • Akhilesh PrasadEmail author
  • Z. A. Ansari


The main objective of this paper is to study the linear canonical wavelet transform (LCWT) on generalized Sobolev space \(B^{\xi ,A}_{p,k}(\mathbb {R})\) and generalized weighted space \(L^{s,p}_{\epsilon ,A}(\mathbb {R})\). Its approximation properties and convergence of convolution for \(F^{A}_{\psi }\) in the space \(B^{\xi ,A}_{p,k}(\mathbb {R})\) are also discussed. Based on these properties, we prove that the LCWT is linear continuous mapping on the spaces of \(F^{*}_{p,A}\) and \( U^{k}_{p,A}\). 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 \(H^{s}_{\epsilon ,A}(\mathbb {R})\) are studied.


Linear canonical transform Linear canonical wavelet transform Canonical convolution Generalized Sobolev spaces Schwartz space Generalized weighted Sobolev space 

Mathematics Subject Classification

43A32 42C40 46E35 46F12 



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Authors and Affiliations

  1. 1.Department of Applied Mathematics, Indian Institute of TechnologyIndian School of MinesDhanbadIndia

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