arXiv subjects
Publications and source records attributed to S. Ludkovsky.
The non-Archimedean spectral theory and spectral integration is developed. The analog of the Stone theorem is proved. Applications are considered for algebras of operators.
Stochastic processes on topological vector spaces over non-Archimedean fields and with transition measures having values in non-Archimedean fields are defined and investigated. For this the non-Archimedean analog of the Kolmogorov theorem is proved. The analogos of Markov and Poisson processes are studied. For Poisson processes the corresponding Poisson measures are considered and the non-Archimedean analog of the Lèvy theorem is proved. Wide classes of stochastic processes are constructed.
$p$-Adic compactifications of geometric loop and diffeomorphism groups of compact manifolds on finite-dimensional spaces over non-Archimedean fields are investigated. Weakened topology is introduced. The structure of newly constructed compact groups is studied. Representations of such profinite groups are discused.
A duality of $κ$-normed topological vector spaces is defined and investigated. For such spaces the analog of the Mackey-Arens theorem is proved. There are investigated cases, when $κ$-normability of a topological vector space implies its local convexity. There are given applications of $κ$-normed spaces for resolutions of differential equations and for approximations of functions in mathematical economy.