Damek-Ricci空间的谱分析
Spectral Analysis on Damek-Ricci Space
摘要：
定义并研究了Damek-Ricci空间NA上紧支撑分布的谱投影算子。利用谱投影算子建立了Paley-Wiener-Schwartz定理和S^{p}（NA）^{#}（0<p<=2）的值域.给出了该算子的L^{2}-估计.为了证明非必要径向函数的Paley-Wiener定理，以Damek-Ricci空间为例，在复平面的单位圆盘上，谱投影算子可以用Paley-Wiener定理类型的解析性和λ中的增长条件唯一地刻画.
英文摘要：
We define and study the spectral projection operator for compactly supported distributions on Damek-Ricci space NA. The Paley-Wiener-Schwartz theorem and the range of S^{p}(NA)^{#}(0<p<=2) via spectral projection operator are established. The L^{2}-estimation for this operator is also given. In order to do the Paley-Wiener theorem for the non necessary radial function, the spectral projection operator can be uniquely characterized by analyticity and growth condition in lambda of Paley-Wiener theorem type on the unit disk of the complex plane as an example of Damek-Ricci space.
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