Associated and quasi associated homogeneous distributions (generalized functions)
| dc.creator | Shelkovich, V. M. | |
| dc.date | 2006-08-27 | |
| dc.date.accessioned | 2026-07-07T07:22:13Z | |
| dc.date.available | 2026-07-07T07:22:13Z | |
| dc.description | In this paper analysis of the concept of {\it associated homogeneous distributions} (generalized functions) is given, and some problems related to these distributions are solved. It is proved that (in the one-dimensional case) there exist {\it only} {\it associated homogeneous distributions} of order $k=1$. Next, we introduce a definition of {\it quasi associated homogeneous distributions} and provide a mathematical description of all quasi associated homogeneous distributions and their Fourier transform. It is proved that the class of {\it quasi associated homogeneous distributions} coincides with the class of distributions introduced by Gel$'$fand and Shilov \cite[Ch.I,§4.]{G-Sh} as the class of {\it associated homogeneous distributions}. For the multidimensional case it is proved that $f$ is a {\it quasi associated homogeneous distribution} if and only if it satisfies the Euler type system of differential equations. A new type of $Γ$-functions generated by quasi associated homogeneous distributions is defined. | |
| dc.identifier | https://arxiv.org/abs/math/0608669 | |
| dc.identifier | http://arxiv.org/abs/math/0608669 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115579 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 46F10 | |
| dc.title | Associated and quasi associated homogeneous distributions (generalized functions) | |
| dc.type | text |