Title

Holomorphic Fock spaces for positive linear transformations

Document Type

Article

Publication Date

1-1-2006

Abstract

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 dμA(z) = √detA/πn e-Re(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.

Publication Source (Journal or Book title)

Mathematica Scandinavica

First Page

262

Last Page

281

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