A unified approach to infinite-dimensional integration-Reference-Cited by-同舟云学术

A unified approach to infinite-dimensional integration

Published:2016-03 Issue:02 Volume:28 Page:1650005
ISSN:0129-055X
Container-title:Reviews in Mathematical Physics
language:en
Short-container-title:Rev. Math. Phys.

Author:

Albeverio S.¹²³,Mazzucchi S.⁴⁵

Affiliation:

1. Institut für Angewandte Mathematik, Endenicher Allee 60, 53115 Bonn, Germany

2. HCM; BIBOS; IZKS, Germany

3. CERFIM (Locarno), Switzerland

4. Dipartimento di Matematica, Università di Trento, via Sommarive 14 I-38123 Trento, Italy

5. INFN-TIFPA, Italy

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, Schrödinger and diffusion equations, as well as higher order hyperbolic and parabolic equations.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129055X16500057

Reference147 articles.

1. Finite Dimensional Approximation Approach to Oscillatory Integrals and Stationary Phase in Infinite Dimensions

2. Oscillatory integrals on Hilbert spaces and Schrödinger equation with magnetic fields

3. Finite Dimensional Approximation Approach to Oscillatory Integrals and Stationary Phase in Infinite Dimensions

4. Oscillatory integrals on Hilbert spaces and Schrödinger equation with magnetic fields

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