A fractional power theory for Hankel transform in \(L^ 2(\mathbb{R}^ +)\)

DOI10.1016/0022-247X(91)90271-ZzbMath0735.44002MaRDI QIDQ1176163

Fiona H. Kerr

Publication date: 25 June 1992

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Hankel transformFourier Cosine and Fourier Sine transformsfractional power theoryfractionalisations

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Fractional derivatives and integrals (26A33)

Related Items (20)

Integral representations of Bargmann type for the \(\beta \)-modified Bergman space on punctured unit disc ⋮ Windowed linear canonical transform and its applications to the time-frequency analysis ⋮ Two-dimensional fractional Fourier transform and some of its properties ⋮ On dual transform of fractional Hankel transform ⋮ The Bessel wavelet transform of distributions in βμ′-space ⋮ Fractionalization of a discrete Hankel transform based on an involutory symmetric kernel matrix ⋮ Canonical Fourier-Bessel transform and their applications ⋮ CHARACTERIZATIONS OF THE INVERSION FORMULA OF THE CONTINUOUS BESSEL WAVELET TRANSFORM OF DISTRIBUTIONS IN Hμ′(ℝ+) ⋮ Fractional Hankel and Bessel wavelet transforms of almost periodic signals ⋮ Hardy type theorems for linear canonical Dunkl transform ⋮ Linear canonical Fourier–Bessel wavelet transform: properties and inequalities ⋮ Prolate spheroidal wave functions associated with the canonical Fourier–Bessel transform and uncertainty principles ⋮ A new perspective on the two-dimensional fractional Fourier transform and its relationship with the Wigner distribution ⋮ Fractional powers of Hankel transforms in the Zemanian spaces ⋮ A unified class of integral transforms related to the Dunkl transform ⋮ A perspective on fractional Laplace transforms and fractional generalized Hankel-Clifford transformation ⋮ Harmonic analysis associated to the canonical Fourier Bessel transform ⋮ A variation on uncertainty principles for quaternion linear canonical transform ⋮ Fractional Jacobi-Dunkl transform: properties and application ⋮ Quantitative uncertainty principles for the canonical Fourier-Bessel transform

Cites Work

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• Namias' fractional Fourier transforms on \(L^ 2\) and applications to differential equations
• On one-parameter unitary groups in Hilbert space
• On Namias's Fractional Fourier Transforms
• A distributional approach to Namias' fractional Fourier transforms
• The Fractional Order Fourier Transform and its Application to Quantum Mechanics
• Fractionalization of Hankel Transforms

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