Related papers: On the geometric properties of the Bessel-Struve k…
The main purpose of the present paper is to ascertain the radii of starlikeness and convexity associated with lemniscate of Bernoulli and the Janowski function, $(1+Az)/(1+Bz)$ for $-1\leq B<A\leq 1,$ of normalized hyper-Bessel function.
New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The…
In this paper, we present an explicit description for the boundary behavior of the Bergman kernel function, the Bergman metric, and the associated curvatures along certain sequences converging to an $h$-extendible boundary point.
The purpose of this paper is to establish that for any compact, connected C^{\infty} Riemannian manifold there exists a robust family of kernels of increasing smoothness that are well suited for interpolation. They generate Lagrange…
For $0<p<\infty$, we give a complete description of nonnegative radial weight functions $\omega$ on the open unit disk $\mathbb{D}$ such that $$ \int_{\mathbb{D}} |f'(z)|^p (1-|z|^2)^{p-2}\omega(z)dA(z)<\infty $$ if and only if $$…
For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a power (possibly fractional) of a defining function, and, more generally, of the…
In this paper we investigate an interesting subclass $\mathcal{BS}(\alpha)$ ($0\leq \alpha<1$) of starlike functions in the unit disk $\Delta$. The class $\mathcal{BS}(\alpha)$ was introduced by Kargar et al. [R. Kargar, A. Ebadian and J.…
We determine the $1$-exponent (according to the Calder\'on-Zygmund definition) of the Brjuno function $B$ everywhere, thus showing that it is a new example of multifractal function. We also discuss various notions of pointwise regularity of…
We consider weighted Bergman spaces $A_\mu^1$ on the unit disc as well as the corresponding spaces of entire functions, defined using non-atomic Borel measures with radial symmetry. By extending the techniques from the case of reflexive…
In this work, we introduce bicomplex Bessel function and analyze its region of convergence. Important properties of the bicomplex Bessel function, such as recurrence relations, integral representations, differential relations are explored.…
A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The Trapezoidal Rule, applied to suitable integral…
The modified Bessel functions $K_{\nu}(z)$, or, for brevity, K-Bessel functions, arise at key places in analytic number theory. In particular, they appear in beautiful arithmetic identities. A survey of these arithmetical identities and…
We study representations of inner functions on the bidisc from a fractional linear transformation point of view, and provide sufficient conditions, in terms of colligation matrices, for the existence of two-variable inner functions. Here…
We prove a limit relation for the Dunkl-Bessel function of type $B_N$ with multiplicity parameters $k_1$ on the roots $\pm e_i$ and $k_2$ on $\pm e_i\pm e_j$ where $k_1$ tends to infinity and the arguments are suitably scaled. It gives a…
Fixed a continuous kernel K on the $d$-dimensional torus, we consider a generalization of the univariate $sk$-spline to the torus, associated with the kernel K. It is proved an estimate which provides the rate of convergence of a given…
We find the radius of starlikeness of order $\alpha$, $0\leq \alpha<1$, of normalized analytic functions $f$ on the unit disk satisfying either $\operatorname{Re}(f(z)/g(z))>0$ or $\left| (f(z)/g(z))-1\right|<1$ for some close-to-star…
The Generalized Bessel Function (GBF) extends the single variable Bessel function to several dimensions and indices in a nontrivial manner. Two-dimensional GBFs have been studied extensively in the literature and have found application in…
New index transforms are investigated, which contain as the kernel products of the Bessel and modified Bessel functions. Mapping properties and invertibility in Lebesgue spaces are studied for these operators. Relationships with the…
Using an orbifold description of the Euclidean BTZ black hole, we show that there is a special relation between the spectrum and the truncated heat kernel of this black hole with the Patterson-Selberg zeta function.
We prove that the Bergman kernel function associated to a finitely connected domain in the plane is given as a rational combination of only three basic functions of one complex variable: an Alhfors map, its derivative, and one other…