Generalized Inequalities for Nonuniform Wavelet Frames in Linear Canonical Transform Domain

Abstract

A constructive algorithm based on the theory of spectral pairs for con- structing nonuniform wavelet basis in L2(R) was considered by Gabardo and Nashed. In this setting, the associated translation set is a spectrum Λ which is not necessar- ily a group nor a uniform discrete set, given Λ = {0,r/N} + 2Z, where N ≥ 1 (an integer) and r is an odd integer with 1 ≤ r ≤ 2N − 1 such that r and N are rel- atively prime and Z is the set of all integers. In this article, we continue this study based on non-standard setting and obtain some inequalities for the nonuniform wavelet system to be a frame associated with linear canonical transform in L2(R). We use the concept of linear canonical transform so that our results generalise and sharpen some well-known wavelet inequalities.