International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 23, Pages 3799-3817

Non-Archimedean valued quasi-invariant descending at infinity measures

S. V. Lüdkovsky

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.