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Central Gaussian convolution semigroups on compact groups: a survey
"... This is a survey article on Brownian motions on compact connected groups and the associated Gaussian convolution semigroups. The emphasize is on infinite dimensional groups such as the infinite dimensional torus and infinite products of special orthogonal groups. We discuss the existence of Brownian ..."
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This is a survey article on Brownian motions on compact connected groups and the associated Gaussian convolution semigroups. The emphasize is on infinite dimensional groups such as the infinite dimensional torus and infinite products of special orthogonal groups. We discuss the existence of Brownian motions having nice properties such as marginales having a continuous density with respect to Haar measure. We relate the existence of these Brownian motions to the algebraic structure of the group. The results we describe reflect the conflicting effects of, on the one hand, the infinite dimensionality and, on the other hand, the compact nature of the underlying group. 1
Analysis on compact Lie groups of large dimension and on connected compact groups
, 2009
"... The study of Gaussian convolution semigroups is a subject at the crossroad between abstract and concrete problems in harmonic analysis. This article suggests selected open problems that are in large part motivated by joint work with Alexander Bendikov. This paper is dedicated to the memory of Andrze ..."
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The study of Gaussian convolution semigroups is a subject at the crossroad between abstract and concrete problems in harmonic analysis. This article suggests selected open problems that are in large part motivated by joint work with Alexander Bendikov. This paper is dedicated to the memory of Andrzej Hulanicki. My first scientific encounter with Andrzej was through his students, which is fitting given the importance they had to him throughout his career. During my Ph.D., I came across the work of Pavel Glowacki (he told me later that he was the referee of my first research paper, published by Studia Mathematica and based on my Ph.D. Thesis). Later, I met Waldemar Hebisch, in Boston, in the late nineteen eighties. In 1991, Andrzej invited me (together with my wife, Cathy) to Wroc̷law for a month. We met for the first time at the Wroc̷law train station where he picked us up, carrying a mathematical book so that we could recognized him. This turned out to be a beginning of a very enjoyable personal and scientific
c ○ World Scientific Publishing Company CENTRAL GAUSSIAN CONVOLUTION SEMIGROUPS ON COMPACT GROUPS: A SURVEY
, 2002
"... Communicated by R. Léandre This is a survey article on Brownian motions on compact connected groups and the associated Gaussian convolution semigroups. The emphasize is on infinite dimensional groups such as the infinite dimensional torus and infinite products of special orthogonal groups. We discus ..."
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Communicated by R. Léandre This is a survey article on Brownian motions on compact connected groups and the associated Gaussian convolution semigroups. The emphasize is on infinite dimensional groups such as the infinite dimensional torus and infinite products of special orthogonal groups. We discuss the existence of Brownian motions having nice properties such as marginales having a continuous density with respect to Haar measure. We relate the existence of these Brownian motions to the algebraic structure of the group. The results we describe reflect the conflicting effects of, on the one hand, the infinite dimensionality and, on the other hand, the compact nature of the underlying group.