Related papers: Multiplier sequences, classes of generalized Besse…
We fully classify completely multiplicative sequences which are given by generalised polynomial formulae, and obtain a similar result for (not necessarily completely) multiplicative sequences under the additional restriction that the…
The notation of generalized Bessel multipliers is obtained by a bounded operator on $\ell^2$ which is inserted between the analysis and synthesis operators. We show that various properties of generalized multipliers are closely related to…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
We introduce and study new modules and spaces of generalized functions that are related to the classical Besov spaces. Various Schwartz distribution spaces are naturally embedded into our new generalized function spaces. We obtain precise…
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…
We study the distribution of zeros of general solutions of the Airy and Bessel equations in the complex plane. Our results characterize the patterns followed by the zeros for any solution, in such a way that if one zero is known it is…
This is the first installment in a series of papers devoted to examining certain aspects of the asymptotic value distribution and distribution of zeros manifested by members of a broad class of linear combinations of L-functions in the…
In the first part of this paper, we express the generalized Bessel function associated with dihedral systems and a constant multiplicity function as a infinite series of confluent Horn functions. The key ingredient leading to this…
The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the…
For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.
A broader class of Hardy spaces and Lebesgue spaces have been introduced recently on the unit circle by considering continuous $\|.\|_1$-dominating normalized gauge norms instead of the classical norms on measurable functions and a Beurling…
In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some…
The Bessel-Neumann expansion (of integer order) of a function $g:\mathbb{C}\rightarrow\mathbb{C}$ corresponds to representing $g$ as a linear combination of basis functions $\phi_0,\phi_1,\ldots$, i.e., $g(z)=\sum_{\ell = 0}^\infty w_\ell…
The goal of this paper is to extend the classical and multiplicative fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function…
Highly oscillatory integrals, such as those involving Bessel functions, are best evaluated analytically as much as possible, as numerical errors can be difficult to control. We investigate indefinite integrals involving monomials in $x$…
We provide an explicit formula for the coefficient polynomials of a Hermite diagonal differential operator. The analysis of the zeros of these coefficient polynomials yields the characterization of generalized Hermite multiplier sequences…
The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal…
We investigate a family of integrals involving modified Bessel functions that arise in the context of neutrino scattering. Recursive formulas are derived for evaluating these integrals and their asymptotic expansions are computed. We prove…
Let $\alpha$ and $\beta$ be two nonnegative integers such that $\beta < \alpha$. For an arbitrary sequence $\{a_n\}_{n\geqslant 1}$ of complex numbers, we consider the generalized Lambert series in order to investigate linear combinations…
In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schr\"odinger-Volkov and Dirac-Volkov solution is expanded into…