On the representation of nuclear Lie groups
The author gives a satisfactory solution to a question of I. M. Gelfand and N. Y. Vilenkin on infinite-dimensional harmonic analysis. They introduced the notion of nuclear Lie group and provided a concrete determination of the continuous unitary representation of such a group in case the underlying locally convex space is nuclear and metrizable. Utilizing Fourier transform of cylindrical probabilities and radonifying bornologies the author is able to give a concrete determination in the general case.
Fourier transform of cylindrical probabilities
scientific article; zbMATH DE number 937041