论文标题
$ \ mathbb {h}^2 $及以后的微分方程的不变系统的溶解度
Solvability of invariant systems of differential equations on $\mathbb{H}^2$ and beyond
论文作者
论文摘要
我们展示了在非紧凑型$ g/k $的对称空间上的向量捆绑包的分布部分的傅立叶变换，可以用于与霍曼德（Hörmander）ehrenpreis-malgrange therorem的证据相比，不变差分方程的系统的可溶性。我们获得了双曲机平面$ \ mathbb {h}^2 $的完整解决性，产品$ \ mathbb {h}^2 \ times \ cdots \ times \ times \ times \ times \ times \ times \ mathbb {h}^2 $和4sbolic 3-space 3-space $ \ mathbb $ \ mathbb {h}^3 $。
We show how the Fourier transform for distributional sections of vector bundles over symmetric spaces of non-compact type $G/K$ can be used for questions of solvability of systems of invariant differential equations in analogy to Hörmander's proof of the Ehrenpreis-Malgrange theorem. We get complete solvability for the hyperbolic plane $\mathbb{H}^2$ and partial results for products $\mathbb{H}^2 \times \cdots \times \mathbb{H}^2$ and the hyperbolic 3-space $\mathbb{H}^3$.
