Two-dimensional fractional Fourier transform and some of its properties

DOI10.1080/10652469.2018.1471689zbMath1393.42011OpenAlexW2803435752MaRDI QIDQ4567910

Ahmed I. Zayed

Publication date: 20 June 2018

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2018.1471689

zbMATH Keywords

fractional Fourier transformPoisson summation formulaconvolution theoremHermite polynomials of two complex variables

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Application of orthogonal and other special functions (94A11) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

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Cites Work

• A novel fractional wavelet transform and its applications
• A fractional power theory for Hankel transform in \(L^ 2(\mathbb{R}^ +)\)
• Fractional powers of Hankel transforms in the Zemanian spaces
• Foundations of time-frequency analysis
• The generalized continuous wavelet transform associated with the fractional Fourier transform
• Unified fractional Fourier transform and sampling theorem
• Analytic properties of complex Hermite polynomials
• On Namias's Fractional Fourier Transforms
• The Fractional Order Fourier Transform and its Application to Quantum Mechanics
• Fractionalization of Hankel Transforms
• Harmonic Analysis in Phase Space. (AM-122)
• Fractional fourier transform of generalized functions
• A class of fractional integral transforms: a generalization of the fractional Fourier transform

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