论文标题
Holbert空间的标准子空间在管域上
Standard subspaces of Hilbert spaces of holomorphic functions on tube domains
论文作者
论文摘要
在本文中，我们研究了管域e + i c^0的矢量值霍尔伯特空间的标准子空间，其中c \ subeq e是在E^{r h}下尖的生成锥形的圆锥体，用于某些内态h \ in \ end（e）中的内态h \，diagonalizable a diagonAlizable a e e e e e e e eigonalizable lorore lor lor eigenvalue lor eigenvalue lor eigenvalue lore。 促进）。该数据指定了一个楔形域W（E，C，H）\ subeq E，我们的主要结果之一表现出相应的标准子空间，为使用这些域上的测试功能生成。 We also investigate aspects of reflection positivity for the triple (E,C,e^{πi h}) and the support properties of distributions on E, arising as Fourier transforms of operator-valued measures defining the Hilbert spaces H. For the imaginary part of these distributions, we find similarities to the well known Huygens' principle, relating to wedge duality in the Minkowski context.有趣的例子是与Euclidean Jordan代数相关的Riesz分布。
In this article we study standard subspaces of Hilbert spaces of vector-valued holomorphic functions on tube domains E + i C^0, where C \subeq E is a pointed generating cone invariant under e^{R h} for some endomorphism h \in \End(E), diagonalizable with the eigenvalues 1,0,-1 (generalizing a Lorentz boost). This data specifies a wedge domain W(E,C,h) \subeq E and one of our main results exhibits corresponding standard subspaces as being generated using test functions on these domains. We also investigate aspects of reflection positivity for the triple (E,C,e^{πi h}) and the support properties of distributions on E, arising as Fourier transforms of operator-valued measures defining the Hilbert spaces H. For the imaginary part of these distributions, we find similarities to the well known Huygens' principle, relating to wedge duality in the Minkowski context. Interesting examples are the Riesz distributions associated to euclidean Jordan algebras.
