Rapid Decay Property with Examples in Crystallographic and Discrete Heisenberg Groups

  • Kankeyanathan Kannan

Abstract

Rapid Decay Property (Property (RD)) provides estimates for the operator norm of those functions (in the left-regular representation) in terms of the Sobolev norm. We provide the examples of length function and related some results. We study the stability of property (RD) with respect to some constructions of groups. We show the some lemmas related for Heisenberg groups. Finally, we show that the following groups have property (RD):
• The Crystallographic groups.
• The Discrete Heisenberg group.

Published
2018-05-11
How to Cite
KANNAN, Kankeyanathan. Rapid Decay Property with Examples in Crystallographic and Discrete Heisenberg Groups. GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR), [S.l.], v. 2, n. 1, may 2018. ISSN 2251-3396. Available at: <http://dl6.globalstf.org/index.php/jmsor/article/view/1510>. Date accessed: 16 dec. 2018.