论文标题
在Fatou定理的欧几里得和真实双曲线空间上
On Pointwise converse of Fatou's theorem for Euclidean and Real hyperbolic spaces
论文作者
论文摘要
在本文中，我们扩展了L. Loomis和W. Rudin的结果，内容涉及上半部空间上正谐波函数的边界行为$ \ r _+^{n+1} $。我们表明，类似的结果对于更一般的近似身份仍然有效。我们将此结果应用于证明对实际双曲空间$ \ mathbb h^n $的Laplace-Beltrami操作员非负征特征函数的边界行为的结果。我们还将证明结果的概括是在\ cite {re}中证明的热方程的大时间行为。我们使用此结果证明了对真正双曲空间的Laplace-Beltrami操作员某些特征函数的渐近行为的结果。
In this article, we extend a result of L. Loomis and W. Rudin, regarding boundary behavior of positive harmonic functions on the upper half space $\R_+^{n+1}$. We show that similar results remain valid for more general approximate identities. We apply this result to prove a result regarding boundary behavior of nonnegative eigenfunctions of the Laplace-Beltrami operator on real hyperbolic space $\mathbb H^n$. We shall also prove a generalization of a result regarding large time behavior of solution of the heat equation proved in \cite{Re}. We use this result to prove a result regarding asymptotic behavior of certain eigenfunctions of the Laplace-Beltrami operator on real hyperbolic space $\mathbb H^n$.
