(1) f ddK0(2zcosd) cos(2„É>) = -í/j_(*)Í.J,(«) + L(z) £-/-,(*)); Jo 4 ^ oV oV J where 7f0 denotes a modified Bessel function of the second kind. Oberhettinger [2] has previously discussed the degenerate cases dl„(z)/dv, v = ± §. The related problem of computing d«/„(z)/óV has been considered by Lee and Radosevich [3], who also present brief numerical tables. References to earlier work may be fo...

Recently D.T. Stoeva proved that if two Bessel sequences in a separable Hilbert space $\mathcal H$ are biorthogonal and one of them is complete H$, then both Riesz bases for H$. This improves well known result where completeness assumed on sequences.
 In this note we present an alternative proof Stoeva's which quite short elementary, based the notion Riesz-Fischer sequences.

In this paper, we show that the matrix elements of some Lorentz group representation operators and bases transform acting in space may be expressed terms modified Bessel–Clifford functions their multi-index analogs introduced by authors via Delerue hyper Bessel functions.

In this paper we consider perturbation of Xd-Bessel sequences, Xdframes, Banach frames, atomic decompositions and Xd-Riesz bases in separable Banach spaces. Equivalence between some perturbation conditions is investigated.

A method is proposed for generating Bessel-like optical beams with arbitrary trajectories in free space. The method involves phase-modulating an optical wavefront so that conical bundles of rays are formed whose apexes write a continuous focal curve with pre-specified shape. These ray cones have circular bases on the input plane; thus their interference results in a Bessel-like transverse field...

This paper introduces the concept of Bessel multipliers. These operators are defined by a fixed multiplication pattern, which is inserted between the analysis and synthesis operators. The proposed concept unifies the approach used for Gabor multipliers for arbitrary analysis/synthesis systems, which form Bessel sequences, like wavelet or irregular Gabor frames. The basic properties of this clas...

Abstract. This paper introduces the concept of Bessel and frame multipliers. These operators are defined by a fixed pattern, called the symbol, which is used after analysis, before synthesis. This concept is a generalization of Gabor multipliers. It allows specialization to any analysis/synthesis systems, that form Bessel sequences, like e.g. wavelet frames. Basic properties of this general cla...

We have analyzed the secondary structure in the region surrounding the initiation codons of both cellular and synthetic versions of ovalbumin mRNA. RNase V1 cleavage sites and structure-dependent, chemically modified bases in cellular ovalbumin mRNA were determined by reverse transcription of hen poly A(+) RNA using ovalbumin-specific, synthetic DNA primers. These results indicate an extensive ...

In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and ...