International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 23, Pages 3799-3817
Non-Archimedean valued quasi-invariant descending at infinity measures
Chair of Applied Mathematics, Moscow State Technical University MIREA, 78 Vernadsky Avenue, Moscow 119454, Russia
Received 18 May 2004; Revised 20 September 2005
Copyright © 2005 S. V. Lüdkovsky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.