论文标题
周期性伪差异操作员的全球性低纤维化三角形系统
Globally hypoelliptic triangularizable systems of periodic pseudo-differential operators
论文作者
论文摘要
本文介绍了属于$ p = d_t + q（t，d_x）$类的全球性低纤维化问题的调查，其中$ q（t，d_x）$是带有条目的$ c_ {j，k，k}（j，k}（t）q_ {j，k k}（j，d_x）$。 $ c_ {j，k}（t）$的系数在圆环$ \ mathbb {t} \ simeq \ simeq \ mathbb {r}/2π\ mathbb {z} $和$ Q_ {该方法在于在矩阵符号$ q（t，ξ）上建立条件，以便将其转换为合适的三角形形式$λ（t，ξ） + \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \λ（t，ξ）$，其中$λ（t，ξ）$是焦点矩阵$ diag $ diag $ diag $ diag $ diag（λ__） λ_{m}（t，ξ））$和$ \ MATHCAL {n}（t，ξ）$是nilpotent上三角矩阵。因此，通过分析特征值$λ_{j}（t，ξ）$及其平均值$λ_{0，j}（ξ）$，将$λ_{j} $，AS $ | eCC配对$ | eCCCed | \ to \ infty $。
This article presents an investigation on the global hypoellipticity problem for systems belonging to the class $P = D_t + Q(t,D_x)$, where $Q(t,D_x)$ is a $m\times m$ matrix with entries $c_{j,k}(t)Q_{j,k}(D_x)$. The coefficients $c_{j,k}(t)$ are smooth, complex-valued functions on the torus $\mathbb{T} \simeq \mathbb{R}/2π\mathbb{Z}$ and $Q_{j,k}(D_x)$ are pseudo-differential operators on $ \mathbb{T}^n$. The approach consists in establishing conditions on the matrix symbol $Q(t,ξ)$ such that it can be transformed into a suitable triangular form $Λ(t,ξ) + \mathcal{N}(t,ξ)$, where $Λ(t,ξ)$ is the diagonal matrix $diag(λ_{1}(t,ξ) \ldots λ_{m}(t,ξ))$ and $\mathcal{N}(t,ξ)$ is a nilpotent upper triangular matrix. Hence, the global hypoellipticity of $P$ is studied by analyzing the behavior of the eigenvalues $λ_{j}(t,ξ)$ and its averages $λ_{0,j}(ξ)$, as $|ξ| \to \infty$.
