Integrated optical phased arrays for generating quasi-Bessel beams are proposed and experimentally demonstrated in a CMOS-compatible platform. Owing to their elongated central beams, Bessel beams have applications in a range of fields, including multiparticle trapping and laser lithography. In this Letter, continuous Bessel theory is manipulated to formulate the phase and amplitude conditions n...

In this article, a family of continuous functions on the unit sphere $$S\subseteq {\mathbb {R}}^{3}$$ is considered as generalization spherical harmonics. The fractalized using linear and bounded operator sphere. Particular values scale vector in iterated function system (IFS) may yield classical We have shown that for different IFS, Bessel sequences, frames, Riesz bases can be established spac...

From Kemp [1], we have a family of confluent q-ChuVandermonde distributions, consisted by three members I, II and III, interpreted as a family of q-steady-state distributions from Markov chains. In this article, we provide the moments of the distributions of this family and we establish a continuous limiting behavior for the members I and II, in the sense of pointwise convergence, by applying a...

we define a new function-valued inner product on l2(g), called ?-bracket product, where g is a locally compact abelian group and ? is a topological isomorphism on g. we investigate the notion of ?-orthogonality, bessel's inequality and ?-orthonormal bases with respect to this inner product on l2(g).

A generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by M. H. Faroughi and R. Ahmadi, is presented in this study. Continuous resolution of the identity (CRI) is introduced, a new family of CRI is constructed, and a number of reconstruction formulas are obtained. Also, new results are given on the duality of continuous fusion fram...

T he Meijer G–functions are a remarkable family G of functions of one variable, each of them determined by finitely many indices. Although each such function is a linear combination of certain special functions of standard type, they seem not to be well known in the mathematical community generally. Indeed they are not even mentioned in most books on special functions, e.g., [1], [18]. Even the...

‎In this paper‎, ‎we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for‎ ‎irreducible admissible representations of orthogonal groups‎, ‎or unitary groups‎. ‎One family is that of local integrals of the doubling method‎, ‎and the other family is‎ ‎that of local integrals expressed in terms of sph...