365 research outputs found
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 , 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
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