Ranges and inversion formulas for spherical mean operator and its dual

DOI10.1006/jmaa.1995.1448zbMath0845.43005OpenAlexW2077209680MaRDI QIDQ1910099

M. Mounir Nessibi, Lakhdar Tannech Rachdi, Khalifa Trimèche

Publication date: 8 September 1996

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

Full work available at URL: https://doi.org/10.1006/jmaa.1995.1448

zbMATH Keywords

integral transformsharmonic analysisBessel functionsinversion formulasgeneralized Fourier transformspherical mean operatortransmutation operatorsPlancherel theorem

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Other transforms and operators of Fourier type (43A32) General integral transforms (44A05)

Related Items (33)

Range descriptions for the spherical mean Radon transform ⋮ Unnamed Item ⋮ Localization of orthonormal sequences in the spherical mean setting ⋮ Spectral theorems associated with the spherical mean two-wavelet multipliers ⋮ Inversion formulas for \(q\)-Riemann-Liouville and \(q\)-Weyl transforms ⋮ \(L^p\)-boundedness of the Littlewood-Paley \(g\)-function associated with the spherical mean operator for \(1<p<+\infty\) ⋮ AN ANALOGUE OF COWLING–PRICE'S THEOREM AND HARDY'S THEOREM FOR THE GENERALIZED FOURIER TRANSFORM ASSOCIATED WITH THE SPHERICAL MEAN OPERATOR ⋮ Maximal operators in the spherical mean setting ⋮ Harmonic analysis and integral transforms associated with a class of a system of partial differential operators ⋮ Mathematics of thermoacoustic tomography ⋮ The Poisson convolution associated with the spherical mean operator ⋮ Toeplitz operators for Stockwell transform related to the spherical mean operator ⋮ On the hemispherical transform in the half-space and related Radon transforms ⋮ The Littlewood-Paley \(g\)-function associated with the spherical mean operator ⋮ Heisenberg type uncertainty principle for the Gabor spherical mean transform ⋮ Weyl transforms associated with the Riemann-Liouville operator ⋮ Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators ⋮ Continuous wavelet transform and uncertainty principle related to the spherical mean operator ⋮ Toeplitz operators for wavelet transform related to the spherical mean operator ⋮ Unnamed Item ⋮ Heisenberg-Pauli-Weyl uncertainty principle for the spherical mean operator ⋮ Some results for the windowed Fourier transform related to the spherical mean operator ⋮ Uncertainty principles for spherical mean \(L^2\)-multiplier operators ⋮ Spectral theorems associated with the spherical mean two-wavelet localization operators ⋮ Boundedness and compactness of the spherical mean two-wavelet localization operators ⋮ Localization operators, time frequency concentration and quantitative-type uncertainty for the continuous wavelet transform associated with spherical mean operator ⋮ Ranges and inversion formulas for the Dunkl intertwining operator and its dual ⋮ Boundedness and compactness of localization operators associated with the spherical mean Wigner transform ⋮ Weyl transform and generalized spectrogram associated with quaternion Heisenberg group ⋮ On the range of the Fourier transform connected with Riemann-Liouville operator ⋮ An inverse source problem connected with thermoacoustic imaging in multi-layer planar medium ⋮ WEYL TRANSFORMS ASSOCIATED WITH THE SPHERICAL MEAN OPERATOR ⋮ Localization operators associated with the spherical mean operator

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