Related papers: On construction of transmutation operators for per…
We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…
This paper presents a representation for the kernel of the composition of multivariate Bernstein-Durrmeyer operators for functions defined on the standard simplex in $\mathbb{R}^d$.
We consider a singularly perturbed semilinear boundary value problem of a general form that allows various types of turning points. A solution decomposition is derived that separates the potential exponential boundary layer terms. The…
Most of the known Fourier transforms associated with the equations of mathematical physics have a trivial kernel, and an inversion formula as well as the Parseval equality are fulfilled. In other words, the system of the eigenfunctions…
A different application of the familiar integral representation for the modifed Bessel function drives to a new Kontorovich-Lebedev-like integral transformation of a general complex index. Mapping and operational properties, a convolution…
The representations of the kernels of the transmutation operator and of its inverse relating the one-dimensional Schr\"odinger operator with the second derivative are obtained in terms of the eigenfunctions of a corresponding…
The paper extends some well-known results for analytic functions onto solutions of the Vekua equation $\partial _{\overline{z}}W=aW+b\overline{W}$ regarding the existence and construction of the Bergman kernel and of the corresponding…
In this paper we study fractional powers of the Bessel differential operator defined on a semiaxis. Some important properties of such fractional powers of the Bessel differential operator are proved. They include connections with Legendre…
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…
The perturbation of the Sturm-Liouville operator on a finite interval with Dirichlet boundary conditions by a convolution operator is considered. Local stability and global unique solvability of the inverse problem of recovering the…
New index transforms of the Lebedev type are investigated. It involves the real part of the product of the modified Bessel functions as the kernel. The boundedness and invertibility are examined for these operators in the Lebesgue weighted…
Discrete analogs of the classical Kontorovich-Lebedev transforms are introduced and investigated. It involves series with the modified Bessel function or Macdonald function $K_{in}(x), x >0, n \in \mathbb{N}, i $ is the imaginary unit, and…
We find the high energy asymptotics for the singular Weyl--Titchmarsh m-functions and the associated spectral measures of perturbed spherical Schr\"odinger operators (also known as Bessel operators). We apply this result to establish an…
In this study we consider perturbative series solution with respect to a parameter {\epsilon} > 0. In this methodology the solution is considered as an infinite sum of a series of functional terms which usually converges fast to the exact…
Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…
This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
We derive differential equations for multiplicative statistics of the Bessel determinantal point process depending on two parameters. In particular, we prove that such statistics are solutions to an integrable nonlinear partial differential…
In the paper we consider the Bessel differential operator L^(\mu)=\dfrac{d^2}{dx^2}+\dfrac{2\mu+1}{x}\dfrac{d}{dx} in half-line (a,\infty), a>0, and its Dirichlet heat kernel p_a^(\mu)(t,x,y). For \mu=0, by combining analytical and…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…