Delest, M. In this paper, we show that the generating function for skew Ferrers diagrams according to their width and area is the quotient of new basic Bessel functions. Nous montrons dans cet article que la fonction g&ntratrice des diagrammes de Ferrers gauches selon les paramktres ptrimttre et aire s'exprime en fonction du quotient des q analogues de deux fonctions de Bessel.

In this paper we uses an I.I. Hirschman-W. Beckner entropy argument to give an uncertainty inequality for the q-Bessel Fourier transform: Fq,vf(x) = cq,v ∫ ∞ 0 f(t)jv(xt, q 2)t2v+1dqt, where jv(x, q) is the normalized Hahn-Exton q-Bessel function.

The aim of this paper is to generalize the q-Heisenberg uncertainty principles studied by Bettaibi et al. 2007, to state local uncertainty principles for the q-Fourier-cosine, the q-Fourier-sine, and the q-Bessel-Fourier transforms, then to provide an inequality of Heisenberg-Weyl-type for the q-Bessel-Fourier transform.

Named essentially after their close relationship with the modified Bessel function K?(z) of second kind, which is known also as Macdonald (or, a slightly different definition, Basset function), so-called polynomials yn(x) and generalized yn(x;?,?) stemmed naturally in some systematic investigations classical wave equation spherical polar coordinates. Our main purpose this invited survey-cum-exp...

Abstract. Starting from a general operator representation in the time-frequency domain, this paper addresses the problem of approximating linear operators by operators that are diagonal or band-diagonal with respect to Gabor frames. A characterization of operators that can be realized as Gabor multipliers is given and necessary conditions for the existence of (Hilbert-Schmidt) optimal Gabor mul...

Starting from a general operator representation in the time-frequency domain, this paper addresses the problem of approximating linear operators by operators that are diagonal or band-diagonal with respect to Gabor frames. A characterization of operators that can be realized as Gabor multipliers is given and necessary conditions for the existence of (Hilbert-Schmidt) optimal Gabor multiplier ap...

We derive the analytical expression of the M(2) factor of a Bessel-Gauss beam of any order and discuss its behavior for high and low values of the width of the Gaussian profile. The case of unapertured Bessel beams can be treated as a limiting case of our analysis.

We address soliton spiraling in optical lattices induced by multiple coherent Bessel beams and show that the dynamic nature of such lattices makes it possible for them to drag different soliton structures, setting them into rotation. We can control the rotation rate by varying the topological charges of lattice-inducing Bessel beams.

A polynomial approximation to Bessel functions that arises from an electromagnetic scattering problem is examined. The approximation is extended to Bessel functions of any integer order, and the relationship to the Taylor series is derived. Numerical calculations show that the polynomial approximation and the Taylor series truncated to the same order have similar accuracies.

We demonstrate a simple and compact laser source that directly produces a Bessel–Gauss beam. The laser resonator consists of a diode-end-pumped Nd:YAG crystal, a planar mirror, and a diffractive mirror designed to phase-conjugate only the lowest-order Bessel–Gauss beam. 2004 Elsevier B.V. All rights reserved. PACS: 42.55.Xi; 42.60.Jf; 42.25.Fx