Semi-classical analysis on H-type groups

Clotilde Fermanian Kammerer, Véronique Fischer

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Abstract

In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodi fferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we define the semi-classical measures of bounded families of square integrable functions which consist of a pair formed by a measure defined on the product of the group and its unitary dual, and by a field of trace class positive operators acting on the Hilbert spaces of the representations. We illustrate the theory by analyzing examples, which show in particular that this semi-classical analysis takes into account thefinite-dimensional representations of the group, even though they are negligible with respect to the Plancherel measure.

Original languageEnglish
Pages (from-to)1057-1086
Number of pages30
JournalScience China Mathematics
Volume62
Issue number6
Early online date15 Apr 2019
DOIs
Publication statusPublished - 1 Jun 2019

Keywords

  • asymptotic analysis
  • H-type groups
  • microlocal analysis
  • semi-classical measures
  • semi-classical pseudodifferential operators
  • Wigner transform
  • 22E30
  • 46L89
  • 35S05

ASJC Scopus subject areas

  • Mathematics(all)

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