2016/02/13 by Marouane Rabaoui, Rabaoui, Marouane
Mathematics · #Advanced Topics in Algebra #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Point processes and geometric inequalities #Representation Theory (math.RT) #math.CA #math.RT
paper · pdf · doi:10.48550/arxiv.1602.04325
16 pages, published in Bulletin des sciences Mathématiques 2015
arxiv created 2016/02/13 · openalex publication_date 2016/02/13 · arxiv updated 2016/02/16 · openalex created_date 2022/08/16 · openalex updated_date 2026/07/28
Using a generalised Bochner type representation for Olshanski spherical pairs, we establish a Lévy-Khinchin formula for the continuous functions of negative type on the space V_∞= M(∞, \mathbb C) of infinite dimensional square complex matrices relatively to the action of the product group K_∞=U(∞)× U(∞). The space V_∞ is the inductive limit of the spaces Vn=M(n, \mathbb C), and the group K_∞ is the inductive limit of the product groups Kn=U(n)× U(n), where U(n) is the unitary group.