Related papers: Sonine Transform Associated to the Bessel-Struve O…
We investigate spectral properties of self-adjoint extensions of the operator $$ G_{\alpha,\beta}=-\Big(\frac{\partial^2}{\partial r^2}+\frac{2\a+1}{r}\frac{\partial}{\partial r} \Big) -r^2 \Big(\frac{\partial^2}{\partial…
In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us to develop the complex spectral theory…
There exist several multivariate extensions of the classical Sonine integral representation for Bessel functions of some index $\mu+ \nu$ with respect to such functions of lower index $\mu.$ For Bessel functions on matrix cones, Sonine…
We prove existence (and simpleness) of the trace for both forward and backward Loewner chains under fairly general conditions on semimartingale drivers. As an application, we show that stochastic Komatu-Loewner evolutions SKLE$_{\alpha,b}$…
Discrete analogs of the Lebedev-Skalskaya transforms are introduced and investigated. It involves series and integrals with respect to the kernels ${\rm Re} K_{\alpha+in}(x), {\rm Im} K_{\alpha+in}(x), x >0, n \in \mathbb{N}, |\alpha | <…
We introduce a family of differential-reflection operators $\Lambda_{A, \varepsilon}$ acting on smooth functions defined on $\mathbb R.$ Here $A$ is a Strum-Liouville function with additional hypotheses and $\varepsilon\in \mathbb R.$ For…
We provide a simple analytic formula in terms of elementary functions for the Laplace transform j_{l}(p) of the spherical Bessel function than that appearing in the literature, and we show that any such integral transform is a polynomial of…
The soft and hard edge scaling limits of $\beta$-ensembles can be characterized as the spectra of certain random Sturm-Liouville operators. It has been shown that by tuning the parameter of the hard edge process one can obtain the soft edge…
The transmutation (transformation) operator associated with the perturbed Bessel equation is considered. It is shown that its integral kernel can be uniformly approximated by linear combinations of constructed here generalized wave…
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure.…
The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of Beta function recently defined by Shadab et al.[19]. Moreover, we establish some results related to the newly…
A new generalization of the modified Bessel function of the second kind $K_{z}(x)$ is studied. Elegant series and integral representations, a differential-difference equation and asymptotic expansions are obtained for it thereby…
We consider the Schr\"odinger operator on the halfline with the potential $(m^2-\frac14)\frac1{x^2}$, often called the Bessel operator. We assume that $m$ is complex. We study the domains of various closed homogeneous realizations of the…
Let $L= -\Delta+ V$ be a Schr\"odinger operator on $\mathbb R^d$, $d\geq 3$, where $V$ is a nonnegative potential, $V\ne 0$, and belongs to the reverse H\"older class $RH_{d/2}$. In this paper, we study the commutators $[b,T]$ for $T$ in a…
The generalized operators of fractional integration involving Appell's function $F_{3}(.) $ due to Marichev-Saigo-Maeda, is applied to the Bessel Struve kernel function $S_{\alpha }\left( \lambda z\right),\lambda ,z\in \mathbb{C}$ to obtain…
In this note, we shall prove a formula for the Fourier transform of spherical Bessel functions over complex numbers, viewed as the complex analogue of the classical formulae of Hardy and Weber. The formula has strong representation…
The aim of this paper is to establish an analogue of Logvinenko-Sereda's theorem for the Fourier-Bessel transform (or Hankel transform) $\ff_\alpha$ of order $\alpha>-1/2$. Roughly speaking, if we denote by $PW_\alpha(b)$ the Paley-Wiener…
We investigate the connections between Weyl-Titchmarsh-Kodaira theory for one-dimensional Schr\"odinger operators and the theory of $n$-entire operators. As our main result we find a necessary and sufficient condition for a one-dimensional…
In this paper, we introduce and investigate a new extension of the beta function by means of an integral operator involving a product of Bessel-Struve kernel functions. We also define a new extension of the well-known beta distribution, the…
Mellin convolution equations acting in Bessel potential spaces are considered. The study is based upon two results. The first one concerns the interaction of Mellin convolutions and Bessel potential operators (BPOs). In contrast to the…