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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.

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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}
}

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9 pages