论文标题
Segal的限制很大 - 巴格曼在球面上变换
Large-$N$ Limit of the Segal--Bargmann Transforms on the Spheres
论文作者
论文摘要
我们研究了Segal-Bargmann在$ s^{n-1}（\ sqrt n）$上的大限制，$（n-1）$ - 半径$ \ sqrt n $的尺寸范围，作为从正常水平上跨越正常水平的Square-Square的单位图，该统一的单位均具有一定的空间，以符合正常水平的空间，以跨越正常的水平，以跨度的空间和整体方面的方面 - 整体方面的空间 - Quadric。特别是，我们给出一个明确的配方，并描述域极限，范围极限以及当$ n $倾向于无穷大时的几何模型。我们表明，限制转换仍然是从极限域到限制范围的统一地图。
We study the large-$N$ limit of the Segal--Bargmann transform on $S^{N-1}(\sqrt N)$, the $(N-1)$-dimensional sphere of radius $\sqrt N$, as a unitary map from the space of square-integrable functions with respect to the normalized spherical measure onto the space of holomorphic square-integrable functions with respect to a certain measure on the quadric. In particular, we give an explicit formulation and describe the geometric models for the limit of the domain, the limit of the range, and the limit of the transform when $N$ tends to infinity. We show that the limiting transform is still a unitary map from the limiting domain onto the limiting range.
