Fock spaces corresponding to positive definite linear transformations

dc.creatorFabec, R.
dc.creatorOlafsson, G.
dc.creatorSengupta, A.
dc.date2003-04-23
dc.date.accessioned2026-07-07T06:28:10Z
dc.date.available2026-07-07T06:28:10Z
dc.descriptionSuppose $A$ 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 $dμ_A(z)=\frac {\sqrt {\det A}} {π^n}e^{-{\rm Re}< Az,z>} dz$ is described in terms of the holomorphic--antiholomorphic 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.
dc.identifierhttps://arxiv.org/abs/math/0304358
dc.identifierhttp://arxiv.org/abs/math/0304358
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97639
dc.subjectFunctional Analysis
dc.subject46E22, 81S10
dc.titleFock spaces corresponding to positive definite linear transformations
dc.typetext

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