Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Consider a Lie group with a unitary representation into a space of holomorphic functions defined on a domain 𝓓 of ℂ and in L²(μ), the measure μ being the unitarizing measure of the representation. On finite-dimensional examples, we show that this unitarizing measure is also the invariant measure for some differential operators on 𝓓. We calculate these operators and we develop the concepts of unitarizing measure and invariant measure for an OU operator (differential operator associated to the representation) in the following elementary cases:
A) The commutative groups (ℝ,+) and (ℝ* = ℝ-0,×).
B) The multiplicative group M of 2×2 complex invertible matrices and some subgroups of M.
C) The three-dimensional Heisenberg group.
A) The commutative groups (ℝ,+) and (ℝ* = ℝ-0,×).
B) The multiplicative group M of 2×2 complex invertible matrices and some subgroups of M.
C) The three-dimensional Heisenberg group.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
9-34
Opis fizyczny
Daty
wydano
2011
Twórcy
autor
- Université de Picardie Jules Verne, INSSET, 48, rue Raspail, 02100 Saint-Quentin (Aisne), UMR6140-CNRS, 33, rue Saint-Leu, 80039 Amiens, France
autor
- Department of Mathematics, Faculty of Science of Tunis, University of Tunis El Manar, Campus Universitaire, 1060, Tunis, Tunisia
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-1