论文标题
在$ diff（s^1）的几何形状上 - $ pseudodivferential oberators基于重归于痕迹
On the geometry of $Diff(S^1)-$pseudodifferential operators based on renormalized traces
论文作者
论文摘要
在本文中，我们研究了一组傅立叶综合运算符的几何形状，这是$ diff（s^1）$的中心扩展，其中包括一组经典的伪差异操作员。考虑了几个亚组，并定义了具有正式伪数算子的相应组。我们调查了该组与受限制的通用线性组$ gl_ {res}的关系，$我们在其中定义了一个右派的伪里人指标，它通过使用重新分配的pseudo-diverential Operators和我们描述了声音的连接类别，扩展了Hilbert-Schmidt Riemannian指标。
In this article, we examine the geometry of a group of Fourier-integral operators, which is the central extension of $Diff(S^1)$ with a group of classical pseudo-differential operators of any order. Several subgroups are considered, and the corresponding groups with formal pseudodifferential operators are defined. We investigate the relationship of this group with the restricted general linear group $GL_{res},$ we define a right-invariant pseudo-Riemannian metric on it that extends the Hilbert-Schmidt Riemannian metric by the use of renormalized traces of pseudo-differential operators, and we describe classes of remarkable connections.
