论文标题
在$ \ mathbb r^n $上的傅立叶积分运算符代数上的痕量扩展和刻度痕迹
Trace Expansions and Equivariant Traces on an Algebra of Fourier Integral Operators on $\mathbb R^n$
论文作者
论文摘要
我们考虑运算符代数$ \ mathscr a $ a $在$ \ mathscr s（\ mathbb r^n）$上，由shubin型pseudodifferential operators，heisenberg-weyl操作员以及Heisenberg-weyl操作员以及对$ \ Mathbb C^n $ to Metapplectiplectilectial的运营商的升降机。 在Shubin演算中的辅助操作员的帮助下，我们在Grubb和Seeley的精神上找到了这些操作员的痕量扩展。此外，我们可以定义一个非交通性残基的推广，该概括为shubin pseudododivential oberators，并在代数上获得一类局部的蚀刻痕迹。
We consider the operator algebra $\mathscr A$ on $\mathscr S(\mathbb R^n)$ generated by the Shubin type pseudodifferential operators, the Heisenberg-Weyl operators and the lifts of the unitary operators on $\mathbb C^n$ to metaplectic operators. With the help of an auxiliary operator in the Shubin calculus, we find trace expansions for these operators in the spirit of Grubb and Seeley. Moreover, we can define a noncommutative residue generalizing that for the Shubin pseudodifferential operators and obtain a class of localized equivariant traces on the algebra.
