On weighted generalized functions associated with quadratic forms

In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with Bessel operator.Comment: 16 page

The general form of the Euler--Poisson--Darboux equation and application of transmutation method

In the paper we find solution representations in the compact integral form to the Cauchy problem for a general form of the Euler--Poisson--Darboux equation with Bessel operators via generalized translation and spherical mean operators for all values of the parameter $k$, including also not studying before exceptional odd negative values. We use a Hankel transform method to prove results in a unified way. Under additional conditions we prove that a distributional solution is a classical one too. A transmutation property for connected generalized spherical mean is proved and importance of applying transmutation methods for differential equations with Bessel operators is emphasized. The paper also contains a short historical introduction on differential equations with Bessel operators and a rather detailed reference list of monographs and papers on mathematical theory and applications of this class of differential equations.Comment: Electronic Journal of Differential Equations, 201

On fractional powers of the Bessel operator on a semiaxis

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 functions for kernel representations, fractional integral operators of Liouville and Saigo, Mellin transform and index laws. Possible applications are indicated to differential equations with fractional powers of the Bessel differential operator.Comment: English version (pp. 1--8) and Russian version (pp. 9--18

Fourier-Bessels transform of a generalized function Vanishing outside a bounded surface

The Fourier-Bessel transform of any generalized function f € S'ev vanishing outside a bounded surface for any test function ψ(х) €Se

Uniqueness of the solution of the cauchy problem for the general Euler-Poisson-Darboux equation

For the general Euler-Poisson-Darboux equation, we prove a theorem on the uniqueness of the solution of the Cauchy problem by the energy metho

On the Issue of Literary Reputation and the Role of the Media in Its Formation (Based on the Prose of Leonid Andreev)

This article examines the problem of literary reputation, which is urgent for today’s literary science, in the context of modern reputation theory. Among the many aspects that together create a public image of the writer, the main focus is on the role of the media. Based on the analysis of the reception of one of the characteristic works, it is  shown how the modern contributed to the creation of the “phenomenon” of Leonid Andreev

Mean-value theorem for B-harmonic functions

We establish a mean value property for the functions which is satisfied to Laplace–Bessel equatio