论文标题
真正的分析伯格曼空间
Real Analytic Bergman Spaces
论文作者
论文摘要
伯格曼空间的通常例子包括在域上闭合全体形态函数的代数。一个人也可以采用此类功能的实际部分，但是从本质上讲，一个正在看同一对象。在本文中，作者表明，如果一个人采用$ z $和$ z $和$（\ bar z）g（z）g（z）$产生的代数，则可以将真实分析性和有限点评估的属性保留在封闭中，其中$ g $是$ g $的全部功能，该功能满足了附近$ \ infty $ \ iffty $的分布。这种情况并不难以满足简单的例子。最终的空间比普通的伯格曼空间大得多。主要的例子是像Fock空间一样具有高斯重量。通过这些真实的分析伯格曼空间的序列，人们可以通过良好的近似值近似。
The usual examples of Bergman spaces consist of the closure of an algebra of holomorphic functions on a domain. One can also take the real part of such functions, but essentially one is looking at the same object. In this paper the author shows that the properties of real analyticity and bounded point evaluation can be preserved under closure in a weighted $L^p$ space, if one takes the algebra generated by $z$ and $(\bar z)g(z)$, where $g$ is an entire function satisfying some condition on the distribution of zeros near $\infty$. The condition is not difficult to satisfy with simple examples. The resulting spaces are much larger than the ordinary Bergman spaces. The main example is with a Gaussian weight like the Fock space. One can get good approximation of the usual Fock space by a sequence of these real analytic Bergman spaces.
