Weyl pseudo-differential operator and Wigner transform on the Poincaré disk

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4 Citations (Scopus)

Abstract

The purpose of this paper is to investigate some relations between the kernel of a Weyl pseudo-differential operator and the Wigner transform on Poincaré disk defined in our previous paper [II]. The composition formula for the class of the operators defined in [II] has not been proved yet. However, some properties and relations, which are analogous to the Euclidean case, between the Weyl pseudo-differential operator and the Wigner transform have been investigated in [II]. In the present paper, an asymptotic formula for the Wigner transform of the kernel of a Weyl pseudo-differential operator as h → 0 is given. We also introduce a space of functions on the cotangent bundle T*D whose definition is based on the notion of the Schwartz space on the Poincaré disk. For an S1-invariant symbol in that space, we obtain a formula to reproduce the symbol from the kernel of the Weyl pseudo-differential operator.

Original languageEnglish
Pages (from-to)29-48
Number of pages20
JournalAnnals of Global Analysis and Geometry
Volume22
Issue number1
DOIs
Publication statusPublished - 2002 Dec 1
Externally publishedYes

Keywords

  • Poincaré disk
  • Weyl pseudo-differential operators
  • Wigner transform

ASJC Scopus subject areas

  • Analysis
  • Political Science and International Relations
  • Geometry and Topology

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