The Experts below are selected from a list of 141 Experts worldwide ranked by ideXlab platform
A R De Pierro - One of the best experts on this subject based on the ideXlab platform.
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reconstruction of a Compactly Supported Function from the discrete sampling of its fourier transform
IEEE Transactions on Signal Processing, 1999Co-Authors: A R De PierroAbstract:We derive a new relation between the discrete Fourier transform of a discrete sampling set of a Compactly Supported Function and its Fourier transform. From this relation, we obtain a new window Function. We then propose a new efficient algorithm to reconstruct the original Function from the discrete sampling of its Fourier transform, which can adopt the fast Fourier transform and has much better accuracy than those in the literature. Several numerical experiments are also provided, illustrating the results.
Mongi Rachdi - One of the best experts on this subject based on the ideXlab platform.
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Some properties of the Riesz potentials in Dunkl analysis
Ricerche Di Matematica, 2015Co-Authors: Chokri Abdelkefi, Mongi RachdiAbstract:In the present paper, we study first the behavior at infinity of the Riesz potential for Dunkl transform of a non Compactly Supported Function. Second, we give for \(1 < p \le q < +\infty \), weighted \(Lp\rightarrow Lq\) boundedness of the Riesz potentials with sufficient conditions. As application, we prove a weighted generalized Sobolev inequality.
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Behavior at infinity for the Riesz potentials associated to the Dunkl operators
arXiv: Functional Analysis, 2013Co-Authors: Chokri Abdelkefi, Mongi RachdiAbstract:In Dunkl theory on Rd which generalizes classical Fourier analysis, we study the behavior at infinity of the Riesz potential of a non Compactly Supported Function.
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Some properties of the Riesz potentials in Dunkl analysis
arXiv: Functional Analysis, 2013Co-Authors: Chokri Abdelkefi, Mongi RachdiAbstract:In Dunkl theory on Rd which generalizes classical Fourier analysis, we study first the behavior at infinity of the Riesz potential of a non Compactly Supported Function. Second, we give for 1
Ursula Molter - One of the best experts on this subject based on the ideXlab platform.
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REFINABLE SHIFT INVARIANT SPACES IN ℝd
International Journal of Wavelets Multiresolution and Information Processing, 2020Co-Authors: Carlos Cabrelli, Sigrid B. Heineken, Ursula MolterAbstract:Let φ : ℝd → ℂ be a Compactly Supported Function which satisfies a refinement equation of the form [Formula: see text] where Γ ⊂ ℝd is a lattice, Λ is a finite subset of Γ, and A is a dilation matrix. We prove, under the hypothesis of linear independence of the Γ-translates of φ, that there exists a correspondence between the vectors of the Jordan basis of a finite submatrix of L = [cAi-j]i,j∈Γ and a finite-dimensional subspace [Formula: see text] in the shift-invariant space generated by φ. We provide a basis of [Formula: see text] and show that its elements satisfy a property of homogeneity associated to the eigenvalues of L. If the Function φ has accuracy κ, this basis can be chosen to contain a basis for all the multivariate polynomials of degree less than κ. These latter Functions are associated to eigenvalues that are powers of the eigenvalues of A-1. Furthermore we show that the dimension of [Formula: see text] coincides with the local dimension of φ, and hence, every Function in the shift-invariant space generated by φ can be written locally as a linear combination of translates of the homogeneous Functions.
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REFINABLE SHIFT INVARIANT SPACES IN ℝd
International Journal of Wavelets Multiresolution and Information Processing, 2005Co-Authors: Carlos Cabrelli, Sigrid B. Heineken, Ursula MolterAbstract:Let φ : ℝd → ℂ be a Compactly Supported Function which satisfies a refinement equation of the form where Γ ⊂ ℝd is a lattice, Λ is a finite subset of Γ, and A is a dilation matrix. We prove, under the hypothesis of linear independence of the Γ-translates of φ, that there exists a correspondence between the vectors of the Jordan basis of a finite submatrix of L = [cAi-j]i,j∈Γ and a finite-dimensional subspace in the shift-invariant space generated by φ. We provide a basis of and show that its elements satisfy a property of homogeneity associated to the eigenvalues of L. If the Function φ has accuracy κ, this basis can be chosen to contain a basis for all the multivariate polynomials of degree less than κ. These latter Functions are associated to eigenvalues that are powers of the eigenvalues of A-1. Furthermore we show that the dimension of coincides with the local dimension of φ, and hence, every Function in the shift-invariant space generated by φ can be written locally as a linear combination of translates of the homogeneous Functions.
Chokri Abdelkefi - One of the best experts on this subject based on the ideXlab platform.
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Some properties of the Riesz potentials in Dunkl analysis
Ricerche Di Matematica, 2015Co-Authors: Chokri Abdelkefi, Mongi RachdiAbstract:In the present paper, we study first the behavior at infinity of the Riesz potential for Dunkl transform of a non Compactly Supported Function. Second, we give for \(1 < p \le q < +\infty \), weighted \(Lp\rightarrow Lq\) boundedness of the Riesz potentials with sufficient conditions. As application, we prove a weighted generalized Sobolev inequality.
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Behavior at infinity for the Riesz potentials associated to the Dunkl operators
arXiv: Functional Analysis, 2013Co-Authors: Chokri Abdelkefi, Mongi RachdiAbstract:In Dunkl theory on Rd which generalizes classical Fourier analysis, we study the behavior at infinity of the Riesz potential of a non Compactly Supported Function.
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Some properties of the Riesz potentials in Dunkl analysis
arXiv: Functional Analysis, 2013Co-Authors: Chokri Abdelkefi, Mongi RachdiAbstract:In Dunkl theory on Rd which generalizes classical Fourier analysis, we study first the behavior at infinity of the Riesz potential of a non Compactly Supported Function. Second, we give for 1
Alexander G. Ramm - One of the best experts on this subject based on the ideXlab platform.
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Formula for the radius of the support of the potential in terms of scattering data
Journal of Physics A, 1998Co-Authors: Alexander G. Ramm, J H Arredondo, B C IzquierdoAbstract:Let q(r), r=|x|, , be a real-valued square-integrable Compactly Supported Function, and be the smallest interval containing the support of q(r). Let be the corresponding scattering amplitude at a fixed positive energy, . Let be the phase shifts at k = 1. It is proved that , provided that q(r) does not change sign in some, arbitrary small, neighbourhood of a.
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Inversion of incomplete radon transform
Applied Mathematics Letters, 1992Co-Authors: Alexander G. Ramm, Alexander KatsevichAbstract:Abstract An analytic formula is derived for inversion of the Radon transform of a Compactly Supported Function from a truncated cone.
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Inversion of the Radon transform with incomplete data
Mathematical Methods in The Applied Sciences, 1992Co-Authors: Alexander G. RammAbstract:The Radon transform R(p, θ), θ∈Sn−1, p∈ℝ1, of a Compactly Supported Function f(x) with support in a ball Ba of radius a centred at the origin is given for all , where is an open set on Sn−1, and all p∈(− ∞, ∞), n≥2. An approximate formula is given to calculate f(x) from the given data.