Generalized inequalities for nonuniform wavelet frames in linear canonical transform domain

Abstract

A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in L2(R) was considered by Gabardo and Nashed. In this setting, the associated translation set is a spectrum ? which is not necessarily a group nor a uniform discrete set, given ? = {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 relatively 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 {f?j,?(x) = (2N)j/2f((2N)jx??)e???A/B (t2??2), j ? Z, ? ? ?}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.