We propose an approach, via relative trace formulae, toward the global restriction problem involvingBessel or Fourier–Jacobi periods on unitary groupsUn×Um , generalizing the work of Jacquet–Rallis form = n−1 (which is a Bessel period). In particular, whenm = 0, we recover a relative trace formula proposed by Flicker concerning Kloosterman/Fourier integrals on quasi-split unitary groups.As evid...

We demonstrate analytically and experimentally that a circular abruptly autofocusing (AAF) Airy beam can be generated by Fourier-transforming an appropriately apodized Bessel beam whose radial oscillations are chirped by a cubic phase term. Depending on the relation between the chirp rate and the focal distance of the Fourier-transforming lens, it is possible to generate AAF beams with one or t...

We propose a new method for the numerical evaluation of the spherical Bessel transform. A formula is derived for the transform by using an integral representation of the spherical Bessel function and by changing the integration variable. The resultant algorithm consists of a set of the Fourier transforms and numerical integrations over a linearly spaced grid of variable k in Fourier space. Beca...

This paper is devoted to the problem of best recovery a fractional power B-elliptic operator function on R+N by its Fourier–Bessel transform known approximately convex set with estimate difference between and approximation in metric L∞. The optimal method has been found. does not use values beyond ball centered at origin.

Keywords: Squared spherical Bessel functions Regularization of Hankel series Gaussian power-law densities Kummer distributions Airy approximation of Bessel integrals a b s t r a c t Bessel integrals of type R 1 0 k lþ2 e Àak 2 ÀðbþixÞk j 2 l ðpkÞdk are studied, where the squared spherical Bessel function j 2 l is averaged with a modulated Gaussian power-law density. These inte-grals define the ...

Abstract This paper deals with Al-Salam fractional q -integral operator and its application to certain -analogues of Bessel functions power series. has been applied various types -Bessel some series special type. It obtained for basic -generating series, -exponential -trigonometric as well. Various results corollaries are provided an this theory.