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, Schr ̈odinger and dif- fusion equations, as well as higher order hyperbolic and parabolic equations.
A unified approach to infinite-dimensional integration / Albeverio, Sergio; Mazzucchi, Sonia. - In: REVIEWS IN MATHEMATICAL PHYSICS. - ISSN 0129-055X. - 2016/28:2(2016), pp. 165000501-165000543. [10.1142/S0129055X16500057]
A unified approach to infinite-dimensional integration
Albeverio, Sergio;Mazzucchi, Sonia
2016
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 Feynman path integrals, Schr ̈odinger and dif- fusion equations, as well as higher order hyperbolic and parabolic equations.| File | Dimensione | Formato | |
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