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Filomat 2023 Volume 37, Issue 12, Pages: 3725-3735
https://doi.org/10.2298/FIL2312725B
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Generalized inequalities for nonuniform wavelet frames in linear canonical transform domain

Bhat Younus M. (Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, India), gyounusg@gmail.com

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 Λ which is not necessarily 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 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 {fμj,λ(x) = (2N)j/2f((2N)jx–λ)e−ιπA/B (t2−λ2), j ∈ Z, λ ∈ Λ}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.

Keywords: Nonuniform wavelets, Wavelet frame, Spectral pair, Linear canonical transform

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