A pseudo-differential calculus on the Heisenberg group
Functional Analysis
2014-02-27 v1 Analysis of PDEs
Representation Theory
Abstract
In this note we present a symbolic pseudo-differential calculus on the Heisenberg group. We particularise to this group our general construction [4,3,2] of pseudo-differential calculi on graded groups. The relation between the Weyl quantization and the representations of the Heisenberg group enables us to consider here scalar-valued symbols. We find that the conditions defining the symbol classes are similar but different to the ones in [1]. Applications are given to Schwartz hypoellipticity and to subelliptic estimates on the Heisenberg group.
Keywords
Cite
@article{arxiv.1402.6615,
title = {A pseudo-differential calculus on the Heisenberg group},
author = {Veronique Fischer and Michael Ruzhansky},
journal= {arXiv preprint arXiv:1402.6615},
year = {2014}
}
Comments
9 pages