Journal of the Mathematical Society of Japan

Infinite dimensional oscillatory integrals as projective systems of functionals


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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.

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

First available in Project Euclid: 27 October 2015

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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]

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


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.

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