25 citations · 100 across the 14 of their papers we have counts for
14 papers
Distributions associated to homogeneous distributions
A. V. Kosyak, V. I. Polischook, V. M. Shelkovich
In this paper we continue to study {\it quasi associated homogeneous distributions \rm{(}generalized functions\rm{)}} which were introduced in the paper by V.M. Shelkovich, Associa…
Wavelet analysis on adeles and pseudo-differential operators
A. Yu. Khrennikov, A. V. Kosyak, V. M. Shelkovich
This paper is devoted to wavelet analysis on adele ring $\bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize fi…
Transport and concentration processes in the multidimensional zero-pressure gas dynamics model with the energy conservation law
S. Albeverio, O. S. Rozanova, V. M. Shelkovich
We introduce integral identities to define delta-shock wave type solutions for the multidimensional zero-pressure gas dynamics Using these integral identities, the Rankine-Hugoniot…
Non-Haar -adic wavelets and their application to pseudo-differential operators and equations
A. Yu. Khrennikov, V. M. Shelkovich
In this paper a countable family of new compactly supported {\em non-Haar} -adic wavelet bases in ${\cL}^2(\bQ_p^n)$ is constructed. We use the wavelet bases in the following ap…
Multidimensional delta-shock waves and the transportation and concentration processes
V. M. Shelkovich
{\it -Shock wave type solutions} in the multidimensional system of conservation laws $$ ρ_t + \nabla\cdot(ρF(U))=0, \qquad (ρU)_t + \nabla\cdot(ρN(U))=0, \quad x\in \bR^n, $$ ar…
-Adic Haar multiresolution analysis and pseudo-differential operators
V. M. Shelkovich, M. Skopina
The notion of {\em -adic multiresolution analysis (MRA)} is introduced. We discuss a ``natural'' refinement equation whose solution (a refinable function) is the characteristic…