Non-Archimedean valued quasi-invariant descending at infinity measures
Measures with values in non-Archimedean fields, which are quasi-invariant and descending at infinity on topological vector spaces over non-Archimedean fields, are studied in this paper. Moreover, their characteristic functionals are considered. In particular, measures having convolution properties l...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2005-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3799 |
| Summary: | Measures with values in non-Archimedean fields, which are
quasi-invariant and descending at infinity on topological vector
spaces over non-Archimedean fields, are studied in this paper.
Moreover, their characteristic functionals are considered. In
particular, measures having convolution properties like classical
Gaussian measures are investigated in the paper. Applications of
such measures to pseudodifferential operators and stochastic
processes are considered. Nevertheless, it is proved that there
does not exist the complete non-Archimedean analog of Gaussian
measures. Theorems about either equivalence or orthogonality of
measures from the considered class are proved. In addition, a
pseudodifferentiability of such measures is investigated. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |