Hormander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

Organisaatiot

  • Imperial College London
  • University of Stuttgart

Kuvaus

In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut476-499
Sivumäärä24
JulkaisuJournal of Fourier Analysis and Applications
Vuosikerta20
Numero3
TilaJulkaistu - kesäkuuta 2014
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 9681860