Irreducible Regular Gaussian Representations of the Groups of the Interval and Circle Diffeomorphisms

We define the analogue of the regular representations for infinite-dimensional groups using quasi-invariant measures on such groups and present the criterium of irreducibility and equivalence of constructed representations for groups of the interval and circle diffeomorphisms. In [A. V. Kosyak, Funktsional Anal. i Prilozhen.24 (1990), 82], a similar construction was done for a certain infinite-dimensional matrix group.