A unified approach to infinite-dimensional integration. (English) Zbl 1339.28018
Summary: 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 Feynman path integrals, Schrödinger and diffusion equations, as well as higher order hyperbolic and parabolic equations.
MSC:
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
| 28C05 | Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures |
| 46G12 | Measures and integration on abstract linear spaces |
Keywords:
integration theory via linear functionals; measure theory on infinite-dimensional spaces; probabilistic representation of solutions of PDEs; stochastic processes; Feynman path integralsReferences:
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