Given a $\sigma $-finite infinite measure space $(\Omega ,\mu )$, it is shown that any Dun\-ford–Schwartz operator $T: \mathcal {L}^1(\Omega )\to )$ can be uniquely extended to the $\mathcal )+\mathcal {L}^\infty (

The application of the Feynman-Kac formula to Polaron models quantum theory leads path measure Brownian motion perturbed by a pair potential that is translation invariant both in space and time. An important problem this context validity central limit theorem infinite volume. We show existence relevant volume limits functional generality includes Frohlich polaron for all coupling constants. pro...

Let G be a connected semisimple Lie group with no compact factors and finite center and let T be a lattice in G (i.e. a discrete subgroup such that G/T has a finite invariant measure). Let n be a representation of G on some vector space V. Borel [Bo] proved that if n is a rational representation and V is finite dimensional then every T-invariant line in V is G-invariant; in fact, this is equiva...

In this paper, we give an extension of the Wendel's theorem on KPC-hypergroups. We also show that every translation invariant mapping is corresponding with a unique positive measure on the KPC-hypergroup.