Spectral Analysis on Damek-Ricci Space
Abstract
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 Sp(NA)#(0<p<=2) via spectral projection operator are established. The L2-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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.