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.
Categories: math-ph math.MP