A unified approach to infinite dimensional integration

TL;DR

This paper introduces a unified framework for infinite dimensional integration that encompasses oscillatory and probabilistic integrals, enabling broad applications across various differential equations.

Contribution

It presents a novel, topologically and measure-theoretically independent approach to infinite dimensional integrals, unifying different integral types under one framework.

Findings

Applicable to Schrödinger and diffusion equations

Extends to higher order hyperbolic and parabolic equations

Provides a linear functional construction of integrals

Abstract

An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear functionals, as much as possible independent of the underlying topological and measure theoretical structure. Various applications are given, including, next to Schr\"odinger and diffusion equations, also higher order hyperbolic and parabolic equations.