Outline Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

A Bessel generator multiplier for a unitary system is a bounded linear operator that sends Bessel generator vectors to Bessel generator vectors. We characterize some special (but useful) Bessel generator multipliers for the unitary systems that are ordered products of two unitary groups. These include the wavelet and the Gabor unitary systems. We also provide a detailed exposition of some of th...

Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...

Optical beam wander is one of the most important issues for free-space optical (FSO) communication. We theoretically derive a beam wander model for Bessel beams propagating in turbulent atmosphere. The calculated beam wander of high order Bessel beams with different turbulence strengths are consistent with experimental measurements. Both theoretical and experimental results reveal that high ord...

We experimentally measured the “self-healing” of the spatially inhomogeneous states of polarization of radial and azimuthal polarized vector Bessel beams. Radial and azimuthal polarized vector Bessel beams were generated via a digital version of Durnin’s method, using a spatial light modulator in concert with a liquid crystal q-plate. As a proof of principle, their intensities and spatially inh...

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 paper, we study a family of analytical probability models for images within the spectral representation framework. First the input image is decomposed using a bank of filters, and probability models are imposed on the filter outputs (or spectral components). A two-parameter analytical form, called a Bessel K form, derived based on a generator model, is used to model the marginal probabi...

We prove that every irreducible, admissible representation π of GSp(4, F ), where F is a non-archimedean local field of characteristic zero, admits a Bessel functional, provided π is not onedimensional. If π is not supercuspidal, we explicitly determine the set of all Bessel functionals admitted by π, and prove that Bessel functionals of a fixed type are unique. If π is supercuspidal, we do the...

In this paper, we extend some known elementary trigonometric inequalities, and their hyperbolic analogues to Bessel and modified Bessel functions of the first kind. In order to prove our main results, we present some monotonicity and convexity properties of some functions involving Bessel and modified Bessel functions of the first kind. We also deduce some Turán and Lazarević-type inequalities ...

Fusion frames are a generalized form of frames in Hilbert spaces. In the present paper we introduce Bessel subfusion sequences and subfusion frames and we investigate the relationship between their operation. Also, the definition of the orthogonal complement of subfusion frames and the definition of the completion of Bessel fusion sequences are provided and several results related with these no...