arXiv subjects
Publications and source records attributed to Marouane Rabaoui.
In this paper, using a generalized Bochner type representation for Olshanski spherical pairs, we prove the boundedness of every $SU(\infty)$-biinvariant continuous function of negative type on the infinite dimensional special linear group $SL(\infty)$.
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 $V_\infty= M(\infty, \mathbb C)$ of infinite dimensional square complex matrices relatively to the action of the product group $K_\infty=U(\infty)\times U(\infty)$. The space $V_\infty$ is the inductive limit of the spaces $V_n=M(n, \mathbb C)$, and the group $K_\infty$ is the inductive limit of the product groups $K_n=U(n)\times U(n)$, where $U(n)$ is the unitary group.
In this paper, we determine the spherical functions of positive type on the inductive limit space of square complex matrices.
In this paper we prove a generalisation of Bochner's theorem. Our result deals with Olshanski's spherical pairs defined as inductive limits of increasing sequences of Gelfand Pairs.