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Fast Numerical Nonlinear Fourier Transforms [PDF]
IEEE Transactions on Information Theory, 2014 The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves.
S. Wahls, H. Poor
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The Fourier Transform on Quantum Euclidean Space [PDF]
, 2010 We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed.
Coulembier, Kevin
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2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2017 We consider the problem of computing the Fourier transform of high-dimensional vectors, distributedly over a cluster of machines consisting of a master node and multiple worker nodes, where the worker nodes can only store and process a fraction of the inputs.
Yu, Qian +2 more
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Transactions of the American Mathematical Society, 1974 If f ( x ) f(x) and g ( x ) g(x) satisfy the equations \[ g ( x ) = d d x ∫ 0 ∞ 1 t ...
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FNFT: A Software Library for Computing Nonlinear Fourier Transforms
Journal of Open Source Software, 2018 The conventional Fourier transform was originally developed in order to solve the heat equation, which is a standard example for a linear evolution equation.
S. Wahls, S. Chimmalgi, P. Prins
semanticscholar +1 more source
On the Fractional Derivative Duality in Some Transforms
Mathematics, 2023 Duality is one of the most interesting properties of the Laplace and Fourier transforms associated with the integer-order derivative. Here, we will generalize it for fractional derivatives and extend the results to the Mellin, Z and discrete-time Fourier
Manuel Duarte Ortigueira +1 more
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Fourier transforms of orbital integrals on the Lie algebra of $\operatorname{SL}_2$ [PDF]
, 2010 The Harish-Chandra--Howe local character expansion expresses the characters of reductive, $p$-adic groups in terms of Fourier transforms of nilpotent orbital integrals on their Lie algebras, and Murnaghan--Kirillov theory expresses many characters of ...
Loren Spice, Loren Spice
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Fourier transforms of Dini-Lipschitz functions
International Journal of Mathematics and Mathematical Sciences, 1986 It is well known that if Lipschitz conditions of a certain order are imposed on a function f(x), then these conditions affect considerably the absolute convergence of the Fourier series and Fourier transforms of f.
M. S. Younis
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Toolbox for the Computation of 2D Fourier Transforms in Polar Coordinates via Maple
Journal of Open Research Software, 2015 The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. A toolbox of functions for the computation of two dimensional Fourier transforms in polar coordinates ...
Edem Dovlo, Natalie Baddour
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Fractional Fourier Transform [PDF]
, 2010 Chapter ...
Ozaktas, Haldun M. +2 more
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