The Gauss and Feynman Distributions on Infinite-Dimensional Spaces over Non-Archimedean Fields

Abstract

By analogy with a finite-dimensional case (Ch. 2) the Gauss and Feynman integrals are defined on the basis of the distribution theory. A variant of the distribution theory is suggested in [69] where the spaces of analytic functions on infinite-dimensional non-Archimedean spaces are used as the spaces of test functions (the functions of an infinite-dimensional argument are often called functionals, but we shall not use this term here). This theory of non-Archimedean spaces is a natural generalization, to the non-Archimedean case, of the theory of analytic infinite-dimensional distributions [38], [43–45], [47], [48] over the field of complex numbers and the supercommutative Banach superalgebras [49], [50], [52], [55], [56].