The purpose of the present paper is to derive the necessary and sufficient condition for the generalized Bessel function (struve function) belonging to the classes Ωλ(g;α, β) and Υ ∗ λ(g;α, β).

Suppose G is a semisimple Lie group with infinite center. As in the finite center case, the tempered spectrum of G consists of families of representations induced from cuspidal parabolic subgroups P = MAN. However, in the infinite center case, the representations of M to be induced are not discrete series, but are relative discrete series which occur in continuous families. In two previous pape...

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...

We review a set of algorithms to evaluate associated Legendre functions off the cut; in particular, we consider prolate spheroidal, oblate spheroidal and toroidal harmonics. A similar scheme can be applied to other families of special functions like Bessel and parabolic cylinder functions; we will describe the corresponding algorithm for the evaluation of parabolic cylinder functions.

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

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...

A Bessel-like beam was generated in a novel all-fiber integrated structure. A concentric ring intensity pattern was achieved by the multimode interference along the coreless silica fiber, which was then focused by the integrated micro-lens to result in a Bessel-like beam. The average beam diameter of 7.5 μm maintained over 500 μm axial length for a continuous wave Yb-doped fiber laser input osc...

the effect of salinity on organic removal and ammonium oxidation in a down-flow hanging sponge reactor was investigated by conducting a long-term continuous experiment over a period of 800 days. the dhs reactor, constructed by connecting three identical units, was fed with artificial wastewater containing 500 mg-n/l of ammonium nitrogen and 1400 mg- cod/l of phenol. salinity of the influent was...