Feynman path integrals over p-adic vector space

摘要

A class of the Schroedinger type equations, with respect to functions defined on the product of [0;∞) ("time") and of the p-adic field ("space"), is considered. In the equation a Vladimirov operator substitutes the standard Lalacian. The main aim of the paper is to get representations of solutions of Cauchy problems for such equations by integrals over Feynman pseudomeasures on paths in the p-adic field (which is spacial domains of the solutions). The significant role is played by some p-adic analogs of Poisson- Maslov measures which are constructed in the paper and are used to get the representations.