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Infinite dimensional oscillatory integrals as projective systems of functionals. (English) Zbl 1334.28024

The authors summarize the contents of this paper in the abstract of the paper as follows: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.

MSC:

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.)
35C15 Integral representations of solutions to PDEs
35Q41 Time-dependent Schrödinger equations and Dirac equations
46M10 Projective and injective objects in functional analysis
60B11 Probability theory on linear topological spaces
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