Invariant measure for some differential operators and unitarizing measure for the representation of a Lie group. Examples in finite dimension

• Autorzy: Hélène Airault , Habib Ouerdiane
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 58J65: Diffusion processes and stochastic analysis on manifolds
• 60J60: Diffusion processes
• 60H07: Stochastic calculus of variations and the Malliavin calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 96
• Numer: 1
• Strony: 9-34

Daty

wydano

2011

Twórcy

autor

Hélène Airault

• Université de Picardie Jules Verne, INSSET, 48, rue Raspail, 02100 Saint-Quentin (Aisne), UMR6140-CNRS, 33, rue Saint-Leu, 80039 Amiens, France

autor

Habib Ouerdiane

• Department of Mathematics, Faculty of Science of Tunis, University of Tunis El Manar, Campus Universitaire, 1060, Tunis, Tunisia

Identyfikatory

DOI

10.4064/bc96-0-1