Abstract. The object of the present paper is to establish an integral formula involving Wright generalized Bessel function (or generalized Bessel-Maitland function) J ν,q (z) defined by Singh et al. [21], which is expressed in the terms of generalized (Wright) hypergeometric functions. Some interesting special cases involving Bessel functions, generalized Bessel functions, generalized Mittag-Le...

We examine some recent results of Bownik on density and connectivity of the wavelet frames. We use orthogonality (strong disjointness) properties of frame and Bessel sequences, and also properties of Bessel multipliers (operators that map wavelet Bessel functions to wavelet Bessel functions). In addition we obtain an asymptotically tight approximation result for wavelet frames.

A variety of transversely accelerating optical beams, such as Airy, Mathieu, and Weber have been proposed intensively studied in the past few decades, while longitudinal acceleration beams free space has considered much less mostly for ultrashort pulses. In this work, we create two-component continuous wave Bessel that exhibit extremely high space, with group velocity changing by a factor 10 ju...

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*...

Recently we introduced the class of highly localized wavepackets (HLWs) as a generalization of optical Bessel-like needle beams. Here we report on the progress in this field. In contrast to pulsed Bessel beams and Airy beams, ultrashort-pulsed HLWs propagate with high stability in both spatial and temporal domain, are nearly paraxial (supercollimated), have fringe-less spatial profiles and thus...

The recursive formulas of modified Bessel functions give the relativistic expressions for energy and momentum. Modified Bessel functions are solutions to a continuous time, one-dimensional discrete jump process. The jump process is analyzed from two inertial frames with a relative constant velocity; the average distance of a particle along the chain corresponds to the distance between two obser...

We show that if (Xs, s ≥ 0) is a right-continuous process, Yt = ∫ t 0 dsXs its integral process and τ = (τl, l ≥ 0) a subordinator, then the time-changed process (Yτl , l ≥ 0) allows to retrieve the information about (Xτl , l ≥ 0) when τ is stable, but not when τ is a gamma subordinator. This question has been motivated by a striking identity in law involving the Bessel clock taken at an indepe...

The pseudodifferential operator (p.d.o.)A(x,D), associated with the Bessel operator d2/dx2 + (1− 4μ2)/4x2, is defined. Symbol class Hm ρ,δ is introduced. It is shown that the p.d.o. associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian spaceHμ into itself. An integral representation of p.d.o. is obtained. Using Hankel convolution Lσ,α-norm continuity of...