论文标题
超偏分布空间中低纤维化差分运算符的零溶液的边界值
Boundary values of zero solutions of hypoelliptic differential operators in ultradistribution spaces
论文作者
论文摘要
我们研究了$ \ Mathbb {r}^{d+1} $的低纤维恒定系数部分差分运算符的零解决方案的超级分布边界值。我们的工作统一并大大扩展了Komatsu和Matsuzawa的各种经典结果，内容涉及超级分布空间中热量函数，谐波函数和零溶液的边界值。我们还提供了Langenbruch [23]的几个结果的新证明，内容涉及$ P（d）$的零解决方案的分布边界值。
We study ultradistributional boundary values of zero solutions of a hypoelliptic constant coefficient partial differential operator $P(D) = P(D_x, D_t)$ on $\mathbb{R}^{d+1}$. Our work unifies and considerably extends various classical results of Komatsu and Matsuzawa about boundary values of holomorphic functions, harmonic functions and zero solutions of the heat equation in ultradistribution spaces. We also give new proofs of several results of Langenbruch [23] about distributional boundary values of zero solutions of $P(D)$.
