Parabolic Type Equations and Markov Stochastic Processes on Adeles |
| |
Authors: | S. M. Torba W. A. Zúñiga-Galindo |
| |
Affiliation: | 1. Department of Mathematics, CINVESTAV del IPN, Unidad Querétaro, Libramiento Norponiente No. 2000, Fracc. Real de Juriquilla, Querétaro, C.P. 76230, Mexico
|
| |
Abstract: | In this paper we study the Cauchy problem for new classes of parabolic type pseudodifferential equations over the rings of finite adeles and adeles. We show that the adelic topology is metrizable and give an explicit metric. We find explicit representations of the fundamental solutions (the heat kernels). These fundamental solutions are transition functions of Markov processes which are adelic analogues of the Archimedean Brownian motion. We show that the Cauchy problems for these equations are well-posed and find explicit representations of the evolution semigroup and formulas for the solutions of homogeneous and non-homogeneous equations. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|