The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on ${\mathbb{R}}^n\oplus {\mathbb{R}}^n$. In this paper we will show that the replacement of this structure by an arbitrary symplectic structure leads to a pseudo-differential calculus of operators acting on functions or distributions defined, not on ${\mathbb{R}}^n$ but rather on ${\mathbb{R}}^n\oplus {\mathbb{R}}^n$. These operators are intertwined with the standard Weyl pseudo-differential operators using an infinite family of partial isometries of $L^2({\mathbb{R}}^n)\to L^2({\mathbb{R}}^{2n})$ indexed by $\mathcal{S}({\mathbb{R}}^n)$. This allows us to obtain spectral and regularity results for our operators using Shubinʼs symbol classes and Feichtingerʼs modulation spaces.

通常的 Weyl 演算与标准辛结构的选择密切相关 ${\mathbb{电阻}}^n\oplus {\mathbb{电阻}}^n$. 在本文中，我们将表明，用任意辛结构替换该结构会导致运算符的伪微分演算作用于定义的函数或分布，而不是作用于定义的函数或分布${\mathbb{电阻}}^n$ 而是在 ${\mathbb{电阻}}^n\oplus {\mathbb{电阻}}^n$. 这些算子与标准的 Weyl 伪微分算子交织在一起，使用的是${升}^2({\mathbb{电阻}}^n)\to {升}^2({\mathbb{电阻}}^{2n})$ 索引 $\mathcal{秒}({\mathbb{电阻}}^n)$. 这使我们能够使用 Shubin 的符号类和 Feichtinger 的调制空间为我们的算子获得频谱和规律性结果。