Geodesic
Vector-valued nonuniform multiresolution analysis associated with linear canonical transform domain
Filomat, Tome 37 (2023) no. 16, p. 5165

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DOI

A generalization of Mallat's classical multiresolution analysis, based on the theory of spectral pairs, was considered in two articles by Gabardo and Nashed. In this setting, the associated translation set is no longer a discrete subgroup of R but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis associated with linear canonical transform (LCT-VNUMRA) where the associated subspace V µ 0 of the function space L 2 R, C M has an orthonormal basis of the form Φ(x − λ)e − ιπA B (t 2 −λ 2) λ∈Λ where Λ = {0, r/N} + 2Z, N ≥ 1 is an integer and r is an odd integer such that r and N are relatively prime. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of vector-valued nonuniform multiresolution analysis starting from a vector refinement mask with appropriate conditions.
DOI : 10.2298/FIL2316165B
Classification : 42C40, 53D22, 94A12, 42A38, 65T60
Keywords: Non-uniform multiresolution analysis, Linear canonical transform, Scaling function, Vector-valued wavelets 
M Younus Bhat; Aamir H Dar. Vector-valued nonuniform multiresolution analysis associated with linear canonical transform domain. Filomat, Tome 37 (2023) no. 16, p. 5165 . doi: 10.2298/FIL2316165B
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     title = {Vector-valued nonuniform multiresolution analysis associated with linear canonical transform domain},
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     year = {2023},
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     doi = {10.2298/FIL2316165B},
     language = {en},
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