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...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3799 |
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| author | S. V. Lüdkovsky |
| author_facet | S. V. Lüdkovsky |
| author_sort | S. V. Lüdkovsky |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fdb516e785524ede9fe27880f30e05ca |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fdb516e785524ede9fe27880f30e05ca2025-02-03T05:51:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005233799381710.1155/IJMMS.2005.3799Non-Archimedean valued quasi-invariant descending at infinity measuresS. V. Lüdkovsky0Chair of Applied Mathematics, Moscow State Technical University MIREA, 78 Vernadsky Avenue, Moscow 119454, RussiaMeasures 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.http://dx.doi.org/10.1155/IJMMS.2005.3799 |
| spellingShingle | S. V. Lüdkovsky Non-Archimedean valued quasi-invariant descending at infinity measures International Journal of Mathematics and Mathematical Sciences |
| title | Non-Archimedean valued quasi-invariant descending at infinity measures |
| title_full | Non-Archimedean valued quasi-invariant descending at infinity measures |
| title_fullStr | Non-Archimedean valued quasi-invariant descending at infinity measures |
| title_full_unstemmed | Non-Archimedean valued quasi-invariant descending at infinity measures |
| title_short | Non-Archimedean valued quasi-invariant descending at infinity measures |
| title_sort | non archimedean valued quasi invariant descending at infinity measures |
| url | http://dx.doi.org/10.1155/IJMMS.2005.3799 |
| work_keys_str_mv | AT svludkovsky nonarchimedeanvaluedquasiinvariantdescendingatinfinitymeasures |