Holomorphic Fock spaces for positive linear transformations - Fabec, R.; Ólafsson, G.; Sengupta, A.N. (Mathematica Scandinavica, 2006)
Suppose A is a positive real linear transformation on a finite dimensional complex inner product space V. The reproducing kernel for the Fock space of square integrable holomorphic functions on V relative to the Gaussian measure dμ_A(z)=A π^ne^-Az,z dz is described in terms of the linear and antilinear decomposition of the linear operator A. Moreover, if A commutes with a conjugation on V, then a restriction mapping to the real vectors in V is polarized to obtain a Segal-Bargmann transform, which we also study in the Gaussian-measure setting.