scholarly journals A discrete Fourier kernel and Fraenkel's tiling conjecture

2005 ◽  
Vol 118 (3) ◽  
pp. 283-304 ◽  
Author(s):  
Ron Graham ◽  
Kevin O'Bryant
Keyword(s):  
Fourier Kernel

scholarly journals A new construction of the Clifford-Fourier kernel

2016 ◽  
Vol 23 (2) ◽  
pp. 462-483 ◽  
Author(s):  
Denis Constales ◽  
Hendrik De Bie ◽  
Pan Lian
Keyword(s):  
New Construction ◽  
Fourier Kernel

A formal solution of certain dual integral equations involving H-functions

1967 ◽  
Vol 63 (1) ◽  
pp. 171-178 ◽  
Author(s):  
R. K. Saxena
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Formal Solution ◽  
Fractional Integration ◽  
Dual Integral Equations ◽  
First Case ◽  
The Common ◽  
The Given ◽  
Fourier Kernel

AbstractThe problem discussed is the formal solution of certain dual integral equations involving H-functions. The method followed is that of fractional integration. The given dual integral equations have been transformed, by the application of fractional integration operators, into two others with a common kernel and the problem is then reduced to solving one integral equation. In the first case the common kernel comes out to be a symmetrical Fourier kernel given earlier by Fox and the formal solution is then immediate. In the second case the common kernel is a generalized Fourier kernel and dual integral equations of this type have recently been studied by Fox.

scholarly journals Identities involving iterated integral transforms

1983 ◽  
Vol 6 (1) ◽  
pp. 111-118
Author(s):  
Cyril Nasim
Keyword(s):  
Linear Combination ◽  
Complex Variable ◽  
Integral Transforms ◽  
Iterated Integral ◽  
Fourier Kernel

A number of identities involving iterated integral transforms are established, making use of the fact that a function which is a linear combination of the Macdonald's functionKν(z), wherezis a complex variable, is a Fourier kernel.

A Fourier kernel

1958 ◽  
Vol 70 (1) ◽  
pp. 297-299 ◽  
Author(s):  
Roop Narain
Keyword(s):  
Fourier Kernel

scholarly journals Fourier Kernel Learning

2012 ◽  
pp. 459-473 ◽  
Author(s):  
Eduard Gabriel Băzăvan ◽  
Fuxin Li ◽  
Cristian Sminchisescu
Keyword(s):  
Kernel Learning ◽  
Fourier Kernel

scholarly journals A Note on Some Definite Integrals of Arthur Erdélyi and George Watson

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 674
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Analytic Continuation ◽  
Current Literature ◽  
Integral Method ◽  
Special Functions ◽  
Contour Integral ◽  
Complex Conjugate ◽  
Definite Integrals ◽  
Special Cases ◽  
Bose Einstein ◽  
Fourier Kernel

This manuscript concerns two definite integrals that could be connected to the Bose-Einstein and the Fermi-Dirac functions in the integrands, separately, with numerators slightly modified with a difference in two expressions that contain the Fourier kernel multiplied by a polynomial and its complex conjugate. In this work, we use our contour integral method to derive these definite integrals, which are given by ∫0∞ie−imx(log(a)−ix)k−eimx(log(a)+ix)k2eαx−1dx and ∫0∞ie−imx(log(a)−ix)k−eimx(log(a)+ix)k2eαx+1dx in terms of the Lerch function. We use these two definite integrals to derive formulae by Erdéyli and Watson. We derive special cases of these integrals in terms of special functions not found in current literature. Special functions have the property of analytic continuation, which widens the range of computation of the variables involved.

scholarly journals The Fractional Clifford-Fourier Kernel

2013 ◽  
Vol 19 (4) ◽  
pp. 683-711 ◽  
Author(s):  
M. J. Craddock ◽  
J. A. Hogan
Keyword(s):  
Fourier Kernel
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