Spectral Analysis on Damek-Ricci Space
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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