Positive definite superfunctions and unitary representations of Lie   supergroups
  For a broad class of Frechet-Lie supergroups we prove that there exists a correspondence between positive definite smooth superfunctions and matrix coefficients of unitary representations. We also give a characterization of linear functionals on the corresponding universal enveloping algebra which correspond to matrix coefficients of analytic unitary representations. 
Karl-Hermann Neeb, Hadi Salmasian
math.RT math-ph math.MP