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.


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
Full Text: DOI Euclid


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