Journal of the Mathematical Society of Japan

Infinite dimensional oscillatory integrals as projective systems of functionals

Sergio ALBEVERIO and Sonia MAZZUCCHI

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Abstract

The theory of infinite dimensional oscillatory integrals and some of its applications are discussed, with special attention to the relations with the original work of K. Itô in this area. A recent general approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented, together with some new developments.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 4 (2015), 1295-1316.

Dates
First available in Project Euclid: 27 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1445951152

Digital Object Identifier
doi:10.2969/jmsj/06741295

Mathematical Reviews number (MathSciNet)
MR3417499

Zentralblatt MATH identifier
1334.28024

Subjects
Primary: 28C05: Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 35C15: Integral representations of solutions 35Q41: Time-dependent Schrödinger equations, Dirac equations 46M10: Projective and injective objects [See also 46A22] 60B11: Probability theory on linear topological spaces [See also 28C20]

Keywords
integration theory via linear continuous functionals measure theory on infinite dimensional spaces Feynman path integrals

Citation

ALBEVERIO, Sergio; MAZZUCCHI, Sonia. Infinite dimensional oscillatory integrals as projective systems of functionals. J. Math. Soc. Japan 67 (2015), no. 4, 1295--1316. doi:10.2969/jmsj/06741295. https://projecteuclid.org/euclid.jmsj/1445951152


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