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.

In the three-dimensional open rectangular domain, problem of identification redefinition function for a partial differential equation with Gerasimov–Caputo-type fractional operator, degeneration, and integral form condition is considered in case 0<??1 order. A positive parameter present mixed derivatives. The solution this studied class regular functions. Fourier series method used, countabl...

This paper develops a Tikhonov regularization theory for nonlinear ill-posed operator equations in Banach spaces. As the main challenge, we consider so-called oversmoothing state sense that penalization is not able to capture true solution regularity and leads infinite penalty value solution. We establish vast extension of Hilbertian convergence through use invertible sectorial operators from h...

We study the inverse spectral problem for Bessel type operators with potential (v(x)): (H_\kappa=-\partial_x^2+\frac{k}{x^2}+v(x)). The is assumed smooth in ((0,R)) and an asymptotic expansion powers logarithms as (x\rightarrow 0^+, v(x)=O(x^\alpha), \alpha >-2). Specifically we show that coefficients of are spectrally determined. This achieved by computing trace resolvent this operator which d...

Abstract In this paper we derive martingale estimating functions for the dimensionality parameter of a Bessel process based on eigenfunctions diffusion operator. Since is non-ergodic and theory developed ergodic diffusions, use space-time transformation formulate our results modified process. We deduce consistency, asymptotic normality discuss optimality. It turns out that function first eigenf...

Motivated by a recent study of Bessel operators in connection with refinement Hardy's inequality involving $ 1/\sin^2(x) on the finite interval (0, \pi) $, we now take closer look at underlying Bessel-type more general inverse square singularities endpoints. More precisely, consider quadratic forms and operator realizations L^2((a, b); dx) associated differential expressions form \begin{documen...

A new method of generating the Bessel functions and ratios of Bessel functions necessary for Mie calculations is presented. Accuracy is improved while eliminating the need for extended precision word lengths or large storage capability. The algorithm uses a new technique of evaluating continued fractions that starts at the beginning rather than the tail and has a built-in error check. The conti...

Recently, the use of Bessel beams in evaluating the possibility of using them for a new generation of ground penetrating radar systems has been considered. Therefore, an analysis of the propagation of Bessel beams in conducting media is worthwhile. We present here an analysis of this type. Specifically, for normal incidence we analyze the propagation of a Bessel beam coming from a perfect diele...

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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 ...