Algebras of symbols associated with the Weyl calculus for Lie group representations

作     者：Beltita, Ingrid Beltita, Daniel 

作者机构：Romanian Acad Sim Stoilow Inst Math Res Unit 1 Bucharest Romania 

出 版 物：《MONATSHEFTE FUR MATHEMATIK》 (数学月刊)

年 卷 期：2012年第167卷第1期

页      面：13-33页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：DGI-FEDER, of the MCYT, Spain [MTM2007-61446] CNCSIS 

主　　题：Weyl calculus Involutive Banach algebra Wiener property Lie group Modulation spaces 

摘      要：We develop our earlier approach to the Weyl calculus for representations of infinite-dimensional Lie groups by establishing continuity properties of the Moyal product for symbols belonging to various modulation spaces. For instance, we prove that the modulation space of symbols M (a,1) is an associative Banach algebra and the corresponding operators are bounded. We then apply the abstract results to two classes of representations, namely the unitary irreducible representations of nilpotent Lie groups, and the natural representations of the semidirect product groups that govern the magnetic Weyl calculus. The classical Weyl-Hormander calculus is obtained for the Schrodinger representations of the finite-dimensional Heisenberg groups, and in this case we recover the results obtained by J. Sjostrand (Math Res Lett 1(2):185-192, 1994).