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It is possible to perform some operations with extrafunctions applying these operations separately to each coordinate. Operations performed in this manner are called regular. It is proved that it is possible to extend several operations…
We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are…
Partial Fourier transforms are used to find explicit formulas for two remarkable fundamental solutions for a generalized Tricomi operator. These fundamental solutions reflect clearly the mixed type of the operator. In order to prove these…
We determine equivalent conditions between the asymptotic coefficients of the Bessel generating functions of a sequence of probability measures and the asymptotic expected values of power sums when their inputs are sampled from these…
An additive map $T$ acting between spaces of vector-valued functions is said to be biseparating if $T$ is a bijection so that $f$ and $g$ are disjoint if and only if $Tf$ and $Tg$ are disjoint. Note that an additive bijection retains…
We write down the generalized Bessel function associated with the root system of type $D$ by means of multivariate hypergeometric series. Our hint comes from the particular case of the Brownian motion in the Weyl chamber of type $D$.
This paper provides a method to study the non-negativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and non-negative, we can study the complex powers…
Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equation, recursive relations, Poisson formula... are also given…
We are concerned with the zeros of the Macdonald functions or the modified Bessel functions of the second kind with real index. By using the explicit expressions for the algebraic equations satisfied by the zeros, we describe the behavior…
In this paper, we are mainly concerned with studying arbitrary unbounded square roots of linear operators as well as some of their basic properties. The paper contains many examples and counterexamples. As an illustration, we give explicit…
Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…
Polynomials which afford nonnegative, real-rooted symmetric decompositions have been investigated recently in algebraic, enumerative and geometric combinatorics. Br\"and\'en and Solus have given sufficient conditions under which the image…
In a previous work, we developed an algorithm for the computation of incomplete Bessel functions, which pose as a numerical challenge, based on the $G_{n}^{(1)}$ transformation and Slevinsky-Safouhi formula for differentiation. In the…
We prove that there is a bijection between the families of regular and non-regular operator monotone functions. As an application we give a new proof of the operator monotonicity of a certain class of functions related to…
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 prove a general version of Bezout's form of the Nullstellensatz for arbitrary fields. The corresponding sufficient and necessary condition only involves the local existence of multi-valued roots for each of the polynomials belonging to…
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…
Using a new technique involving integration it is possible to find the exact roots of simple functions. In this case, simple functions are defined as smooth functions having an inverse, and that inverse having an antiderivative. This…
The matrix-valued {Bezout-corona} problem $G(z)X(z)=I_m$, $|z|<1$, is studied in a Wiener space setting, that is, the given function $G$ is an analytic matrix function on the unit {disc} whose Taylor coefficients are absolutely summable and…
Sufficient conditions are determined on the parameters such that the generalized and normalized Bessel function of the first kind and other related functions belong to subclasses of starlike and convex functions defined in the unit disk…