论文标题
$ NA $组的本征函数的全体形态扩展
Holomorphic extensions of eigenfunctions on $NA$ groups
论文作者
论文摘要
令$ x = g/k $为非竞争类型的Riemannian对称空间。鉴于Iwasawa分解$ g = Nak的底层半圣母谎言组，我们还可以将$ x $视为可解决的扩展名$ s = na $的iwasawa Group $ n $的Na $，这是$ h $ type Group。在这项工作中，我们研究了$ s $上的laplace-beltrami操作员$Δ_s$ to $ s $ on $ s $ to nitpotent group $ n $的综合中的$Δ_s$的全体形态可扩展性。对于任何$ h $ type $ n $，我们也可以做同样的事情，不一定是iwasawa集团。结果是通过利用与相应$ n $上的Laplacian或Sublaplacian的扩展问题解决方案的连接来实现的。
Let $ X = G/K $ be a rank one Riemannian symmetric space of noncompact type. In view of the Iwasawa decomposition $ G = NAK $ of the underlying semisimple Lie group, we can also view $ X $ as the solvable extension $ S = NA $ of the Iwasawa group $ N$ which is known to be a $H$-type group. In this work we study the holomorphic extendability of eigenfunctions of the Laplace-Beltrami operator $ Δ_S$ on $ S $ to certain domains in the complexification of the nilpotent group $ N$. We can also do the same for any $H$-type group $ N $ not necessarily an Iwasawa group. The results are accomplished by making use of the connection with solutions of the extension problem for the Laplacian or the sublaplacian on the corresponding $ N$.
