Fock spaces corresponding to positive definite linear transformations
| dc.creator | Fabec, R. | |
| dc.creator | Olafsson, G. | |
| dc.creator | Sengupta, A. | |
| dc.date | 2003-04-23 | |
| dc.date.accessioned | 2026-07-07T06:28:10Z | |
| dc.date.available | 2026-07-07T06:28:10Z | |
| dc.description | 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 $dμ_A(z)=\frac {\sqrt {\det A}} {π^n}e^{-{\rm Re}< Az,z>} dz$ 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.identifier | https://arxiv.org/abs/math/0304358 | |
| dc.identifier | http://arxiv.org/abs/math/0304358 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97639 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46E22, 81S10 | |
| dc.title | Fock spaces corresponding to positive definite linear transformations | |
| dc.type | text |