Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 67, Number 4 (2015), 1295-1316.
Infinite dimensional oscillatory integrals as projective systems of functionals
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.
J. Math. Soc. Japan, Volume 67, Number 4 (2015), 1295-1316.
First available in Project Euclid: 27 October 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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