In this paper we introduce continuous $g$-Bessel multipliers in Hilbert spaces and investigate some of their properties. We provide some conditions under which a continuous $g$-Bessel multiplier is a compact operator. Also, we show the continuous dependency of continuous $g$-Bessel multipliers on their parameters.

in this paper we introduce continuous $g$-bessel multipliers in hilbert spaces and investigate some of their properties. we provide some conditions under which a continuous $g$-bessel multiplier is a compact operator. also, we show the continuous dependency of continuous $g$-bessel multipliers on their parameters.

We present a Matlab program that computes infinite range integrals of an arbitrary product of Bessel functions of the first kind. The algorithm uses an integral representation of the upper incomplete Gamma function to integrate the tail of the integrand. This paper describes the algorithm and then focuses on some implementation aspects of the Matlab program. Finally we mention a generalisation ...

We formulate a refined version of the global Gan–Gross–Prasad conjecture for general Bessel models, extending the work of Ichino–Ikeda and R. N. Harris in the co-rank 1 case. It is an explicit formula relating the automorphic period of Bessel type and the central value of certain L-function. To support such conjecture, we provide two examples for pairs SO5 SO2 and SO6 SO3 (both co-rank 3) in th...

We provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer. Some interesting special cases and applications of this result are obtained. In particular, we give a short proof of a recent result of A. A. R. Neves et al. regarding the analytical evaluation of an integral of a...

The authors apply a certain novel technique based on the combined use of operational methods and of some special multivariable and multiindex polynomials to derive several families of generating functions involving the products of Bessel and related functions. The possibility of extending this technique to the derivation of generating functions of hybrid nature (involving, for example, the prod...

We provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer. Some interesting special cases and applications of this result are obtained. In particular, we give a short proof of a recent result of A. A. R. Neves et al. regarding the analytical evaluation of an integral of a...

In this work, we extend the analytic treatment of Bessel functions of large order and/or argument. We examine uniform asymptotic Bessel function expansions and show their accuracy and range of validity. Such situations arise in a variety of applications, in particular the Fourier transform of the gravitational wave signal from a pulsar. The uniform expansion we consider here is found to be vali...

In the paper, the authors verify the complete monotonicity of the difference e − ψ′(t) on (0,∞), compute the completely monotonic degree and establish integral representations of the remainder of the Laurent series expansion of e, and derive an inequality which gives a lower bound for the first order modified Bessel function of the first kind. These results show us some new properties and relat...

The connection between the Bessel discrete variable basis expansion and a specific form of an orthogonal set of Jacobi polynomials is demonstrated. These so-called Zernike polynomials provide alternative series expansions of suitable functions over the unit interval. Expressing a Bessel function in a Zernike expansion provides a straightforward method of generating series identities. Furthermor...