Unitarising measures for the representations of affine group and associated invariant operators

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• 作者：H. Airault ; S. Jendoubi ; H. Ouerdiane
• 关键词：primary ; 58D20 ; 58J65 ; secondary ; 17B15 ; 22E45 ; 43A85
• 刊名：Bulletin des Sciences Mathematiques
• 出版年：2013
• 出版时间：September, 2013
• 年：2013
• 卷：137
• 期：6
• 页码：775-790
• 全文大小：210 K

文摘

Let G denote the group of affine transformations on , or one of its subgroups such as the translation group or the Euclidean motion group. In this paper, we study unitarisability of holomorphic representations T of G into the space of square integrable -valued functions with respect to a positive real measure ¦Ì with support in a domain D in . Moreover, we investigate the infinitesimal representation approach of a unitary representation on the Lie algebra of G in order to determine a class of second-order differential operators (called of Ornstein-Uhlenbeck type) invariant with respect to the unitarising measures ¦Ì.