Related papers: One some differential subordination involving the …
In a recent paper we unified Bessel functions of different orders .Here we extend the unification to other linairely independant solutions to Bessel equation, Neumann's and Hankel's functions
The aim of this work is to study new functions arising from the limit transition of the Jackson's $q$-Bessel functions when $q\rightarrow -1$. These functions coincide with the $cas$ function for particular values of their parameters. We…
We present a systematic study of the family of positive definite (p.d.) kernels with the use of their associated feature maps and feature spaces. For a fixed set $X$, generalizing Loewner, we make precise the corresponding partially ordered…
In this note we prove that the reproducing kernel of a Hilbert space satisfying the division property has integrable form, is locally of trace class, and the Hilbert space itself is a Hilbert space of holomorphic functions.
Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…
Targeting at sparse multi-task learning, we consider regularization models with an $\ell^1$ penalty on the coefficients of kernel functions. In order to provide a kernel method for this model, we construct a class of vector-valued…
We prove new bounds for Bessel heat kernels and Bessel heat kernels subordinated by stable subordinators. In particular, we provide a 3G inequality in the subordinated case.
In this paper, we deal with some geometric properties including starlikeness and convexity of order $\alpha$ of Jackson's second and third $q$-Bessel functions which are natural extensions of classical Bessel function $J_{\nu}$. In additon,…
A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to other types of operators. In place of the…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
This survey paper reports on the properties of the fourth-order Bessel-type linear ordinary differential equation, on the generated self-adjoint differential operators in two associated Hilbert function spaces, and on the generalisation of…
Under different assumptions on the potential functions $b$ and $c$, we study the fractional equation $\left( I-\Delta \right)^{\alpha} u = \lambda b(x) |u|^{p-2}u+c(x)|u|^{q-2}u$ in $\mathbb{R}^N$. Our existence results are based on compact…
Let $q_1$ and $q_2$ belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions $p$ to satisfy the double…
The article discusses the fractional powers of the Bessel operator and their numerical implementation. An extensive literature is devoted to the study of fractional powers of the Laplace operator and their applications. Such degrees are…
The Humbert-Bessel are multi-index functions with various applications in electromagnetism. New families of functions sharing some similarities with Bessel functions are often introduced in the mathematical literature, but at a closer…
Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…
Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However,…
In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary…
The primary objective of this work is to obtain some sufficient conditions so that normalized Gauss hypergeometric function satisfies exponential starlikeness and convexity in the unit disk. Moreover, conditions on parameter of this…
By studying cohomological quantum mechanics on the punctured plane,we were led to identify (reduced) Bessel functions with homotopic loops living on the plane.This identification led us to correspondence rules between exponentials and…