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 ...

Motivated by G. H. Hardy's 1939 results [4] on functions orthogonal with respect to their real zeros λn, n = 1, 2,. .. , we will consider, within the same general conditions imposed by Hardy, functions satisfying an orthog-onality with respect to their zeros with Jacobi weights on the interval (0, 1), that is, the functions f (z) = z ν F (z), ν ∈ R, where F is entire and Z 1 0 f (λnt)f (λmt)t α...

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...

In this paper we show that every g-frame for a Hilbert space H can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. We also show that every g-frame can be written as a sum of two tight g-frames with g-frame bounds one or a sum of a g-orthonormal basis and a g-Riesz basis for H . We further give necessary and sufficient conditions on g-Besse...

in this paper, the notion of cyclic $varphi$-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. meantime, an example is provided toillustrate this theorem. the main result shows that a self-mappingon a g-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic $varphi$-contraction. afterwards, some results inco...