BARGMANN'S VERSUS FOR FRACTIONAL FOURIER TRANSFORMS AND APPLICATION TO THE QUATERNIONIC FRACTIONAL HANKEL TRANSFORM

We present a general formalism a la Bargmann for constructing fractional Fourier transform associated to specific class of integral transforms on separable Hilbert spaces. As concrete application, we consider the quaternionic fractional Fourier transform on the real half-line and associated to the h...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 12; no. 4; p. 1356
Main Authors Elkachkouri, A, Ghanmi, A, Hafoud, A
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.09.2022
Elman Hasanoglu
Subjects
Eigenvalues
Fourier transformations
Fourier transforms
Hilbert space
Integral transforms
Mathematical research
Mathematics
Polynomials
Morocco
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Summary:We present a general formalism a la Bargmann for constructing fractional Fourier transform associated to specific class of integral transforms on separable Hilbert spaces. As concrete application, we consider the quaternionic fractional Fourier transform on the real half-line and associated to the hyperholomorphic second Bargmann transform for the slice Bergman space of second kind. This leads to an extended version of the well-known fractional Hankel transform. Basic properties are derived including inversion formula and Plancherel identity. Keywords: Fractional Fourier transform; Fractional Hankel transform; Slice hyperholomorphic Bergman space; Second Bargmann transform; Laguerre polynomials; Bessel functions. AMS Subject Classification: 30G35.
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ISSN:2146-1147
2146-1147