Geodesic
Generalized inequalities for nonuniform wavelet frames in linear canonical transform domain
Filomat, Tome 37 (2023) no. 12, p. 3725

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DOI

A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in L 2 (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} + 2 Z, 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 µ j,λ (x) = (2N) j/2 f (2N) j x − λ e − ιπA B (t 2 −λ 2) , j ∈ Z, λ ∈ Λ to be a frame associated with linear canonical transform in L 2 (R). We use the concept of linear canonical transform so that our results generalise and sharpen some well-known wavelet inequalities.
DOI : 10.2298/FIL2312725B
Classification : 42C40, 42C15, 43A70, 11S85
Keywords: Nonuniform wavelets, Wavelet frame, Spectral pair, Linear canonical transform 
M Younus Bhat. Generalized inequalities for nonuniform wavelet frames in linear canonical transform domain. Filomat, Tome 37 (2023) no. 12, p. 3725 . doi: 10.2298/FIL2312725B
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     title = {Generalized inequalities for nonuniform wavelet frames in linear canonical transform domain},
     journal = {Filomat},
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     year = {2023},
     volume = {37},
     number = {12},
     doi = {10.2298/FIL2312725B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2312725B/}
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