The composition of linear canonical wavelet transforms on generalized function spaces

Prasad, Akhilesh; Ansari, Z. A.

doi:10.2298/fil2012123p

Cited by 2 publications

(2 citation statements)

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“…Recently, some interesting works involving LCT associated with wavelet or wave packet transform have been reported in a distributional sense in previous studies. [6][7][8][9][10][11] An LCT is a family of four parameters…”

Section: Introductionmentioning

confidence: 99%

“…It has been found as a powerful mathematical tool and has wide applications in quantum theory, signal processing, and image processing, to name a few. Recently, some interesting works involving LCT associated with wavelet or wave packet transform have been reported in a distributional sense in previous studies 6–11 . An LCT is a family of four parameters

([], \begin{matrix} center center \\ array α & array β \\ array γ & array δ \end{matrix})

and can be represented in several ways 7,12–15 ; most easily, it can be parameterized by a 2 × 2 matrix with determinant one (an element of the special linear group

S L_{2} false(ℝ false)

).…”

Section: Introductionmentioning

confidence: 99%

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A framework of linear canonical transform on pseudo‐differential operators and its application

Kumar

Pradhan

2021

Math Methods in App Sciences

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The primary aim of this paper is to define a class of pseudo‐differential operators (PDOs) involving linear canonical transform (LCT) associated with the symbol b(x, y). An integral representation of PDOs Pbα,β,γ,δ is given. Boundedness of the composition of operators normalΔx,α,βk and Pbα,β,γ,δ are derived. Further, new integral operators Pbα,β,γ,δ are defined, and their boundedness properties are also investigated. The secondary aim is to find some applications of LCT to solve the boundary value problems of generalized partial differential equations and obtain their solution in closed form. Furthermore, particular cases of these differential equations are discussed, and demonstration of these equations' solutions are shown graphically.

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Section: Introductionmentioning

confidence: 99%

([], \begin{matrix} center center \\ array α & array β \\ array γ & array δ \end{matrix})

and can be represented in several ways 7,12–15 ; most easily, it can be parameterized by a 2 × 2 matrix with determinant one (an element of the special linear group