Reflection positivity and Hankel operators— The multiplicity free case

We analyze reflection positive representations in terms of Hankel operators. This is motivated by the fact that operators are described their Carleson measures, whereas compatibility condition between and Hilbert spaces quite intricate. leads us to concept a representation triples (G,S,τ), where G group, τ an involutive automorphism S⊆G subsemigroup with τ(S)=S−1. For (Z,N,−idZ), corresponding operators, (R,R+,−idR), one-parameter groups, we show every can be made slight change scalar product. A key method consists using measure μH on R+ defined operator H H2(C+) define Pick function whose imaginary part, restricted axis, provides symbol for H.