Results 61 to 70 of about 1,148 (183)

Uniform convergence of Hankel transforms [PDF]

Journal of Mathematical Analysis and Applications, 2018
We investigate necessary and/or sufficient conditions for the pointwise and uniform convergence of the weighted Hankel transforms $$\mathcal{L}^α_{ν,μ}f(r) = r^μ\int_0^\infty (rt)^νf(t) j_α(rt)\, dt, \quad α\geq -1/2, \quad r\geq 0, $$ where $ν,μ\in \mathbb{R}$ are such that $0\leq μ+ν\leq α+3/2$.
openaire   +3 more sources

Calculation of Sommerfeld Integrals in Dipole Radiation Problems

Mathematics
This article proposes asymptotic methods for calculating Sommerfeld integrals, which enable us to calculate the integral using the expansion of a function into an infinite power series at the saddle point, where the role of a rapidly oscillating function
Seil Sautbekov, Merey Sautbekova, Kuralay Baisalova, Mustakhim Pshikov   +3 more
doaj   +1 more source

A distributional Hardy transformation

International Journal of Mathematics and Mathematical Sciences, 1979
The Hardy's F-transform F(t)=∫0∞Fv(ty)yf(y)dy is extended to distributions. The corresponding inversion formula f(x)=∫0∞Cv(tx)tF(t)dt is shown to be valid in the weak distributional sense.
R. S. Pathak, J. N. Pandey
doaj   +1 more source

An efficient discrete Hankel transform based on convolutional Gaussian fast Fourier transform

Earth, Planets and Space
The numerical evaluation of Hankel transforms is fundamental to electromagnetic (EM) geophysics. Typically, this problem is addressed via two distinct paradigms: the digital linear filter (DLF) method, prioritized for its computational speed, and direct ...
Guanzheng Tian, Yuguo Li
doaj   +1 more source

Green's function for the lossy wave equation

Revista Brasileira de Ensino de Física
Using an integral representation for the first kind Hankel (Hankel-Bessel Integral Representation) function we obtain the so-called Basset formula, an integral representation for the second kind modified Bessel function.
R. Aleixo, E. Capelas de Oliveira
doaj   +1 more source

An Accurate MHD Flux Solutions of a Viscose Fluid and Generalized Burgers' Model fluxwithin an Annular Pipe Under Sinusoidal Pressure

Ibn Al-Haitham Journal for Pure and Applied Sciences, 2018
The aim of this work presents the analytical studies of both the magnetohydrodynamic (MHD) flux and flow of the non-magnetohydro dynamic (MHD) for a fluid of generalized Burgers’ (GB) withinan annular pipe submitted under Sinusoidal  Pressure (SP ...
Hanan F. Qasim
doaj   +1 more source

New characterizations for Hankel transformable spaces of Zemanian

International Journal of Mathematics and Mathematical Sciences, 1996
In this paper we obtain new characterizations of the Zemanian spaces Hμ, and H′μ.
J. J. Betancor
doaj   +1 more source

The Boas Problem on Hankel Transforms [PDF]

Journal of Fourier Analysis and Applications, 2019
Norm equivalences between a function and its Hankel transform are studied both in the context of weighted Lebesgue spaces with power weights, and in Lorentz spaces. Boas-type results involving real-valued general monotone functions are obtained. Corresponding results for the Fourier transform are also given.
openaire   +3 more sources

A Nonuniform Fast Hankel Transform

SIAM Journal on Scientific Computing
We describe a fast algorithm for computing discrete Hankel transforms of moderate orders from $n$ nonuniform points to $m$ nonuniform frequencies in $O((m+n)\log\min(n,m))$ operations. Our approach combines local and asymptotic Bessel function expansions with nonuniform fast Fourier transforms.
Paul G. Beckman, Michael O'Neil
openaire   +2 more sources

Identities involving iterated integral transforms

International Journal of Mathematics and Mathematical Sciences, 1983
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 function Kν(z), where z is a complex variable, is a Fourier kernel.
Cyril Nasim
doaj   +1 more source