Probability Distributions on Topological Groups

Sazonov, V. V.; Tutubalin, V. N.

doi:10.1137/1111001

Cited by 54 publications

(20 citation statements)

References 31 publications

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“…An early reference and, indeed, one of the sources of the problems mentioned above is [19]. The first important result directly related to Problems 4-7 above is the fact that A Haar (µ) = 0 for any Gaussian measure µ on a locally compact connected group G unless G is locally connected and admits a countable basis for its topology (for this result due to Heyer and Siebert, see [7,13] and the references therein).…”

Section: Discussion Of Problems 4-7mentioning

confidence: 99%

“…This type of problem already appears in [19]. A well-known theorem (the Hájek-Feldman dichotomy) asserts that two Gaussian measures on a Hilbert space are either absolutely continuous or singular with respect to each other (this is the solution of the linear version of the problem) but the (infinite-dimensional) group version is open even for abelian compact groups (e.g., T ∞ ).…”

Section: Some Open Problemsmentioning

confidence: 99%

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Analysis on compact Lie groups of large dimension and on connected compact groups

Saloff‐Coste

2010

Colloq. Math.

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Abstract. 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 Pawe l G lowacki (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 Wroc law for a month. We met for the first time at the Wroc law train station where he picked us up, carrying a mathematical book so that we could recognize him. This turned out to be a beginning of a very enjoyable personal and scientific relation with Andrzej, his many students and collaborators, and with the Mathematical Institute in Wroc law. As many others, I benefited from attending the conferences and schools organized by Andrzej's group in Tuczno and, later, in Zakopane. My first Ph.D. student, AndrzejŻuk, wrote a Master thesis under Andrzej's supervision in Wroc law before following Andrzej's suggestion to work with me in Toulouse (in fact,Żuk prepared his thesis under the joint supervision of Andrzej and myself, spending half his time in Toulouse and the other half in Wroc law, as required by his doctoral fellowship). Throughout his career, Andrzej, in addition to pursuing his own research in mathematics, put a tremendous energy into organizing and supporting mathematics in Poland and in Wroc law. He maintained many long term scientific international relations, including during periods when it was not necessarily an easy thing to do. He, relentlessly, 2010 Mathematics Subject Classification: 22A10, 43A70, 60B15.

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Section: Discussion Of Problems 4-7mentioning

confidence: 99%

Section: Some Open Problemsmentioning

confidence: 99%

Analysis on compact Lie groups of large dimension and on connected compact groups

Saloff‐Coste

2010

Colloq. Math.

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“…In other words, a measure µ ∈ M + is -infinitely divisible if and only if 15) where v(z) ∈ C. Let us formulate the limit problem for multiplicative free convolution in the case of measures µ ∈ M * . for every ε > 0.…”

Section: (22)mentioning

confidence: 99%

Limit theorems in free probability theory II

Chistyakov

Götze

2008

Open Mathematics

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“…A generalization of characteristic functionals, defined for one-dimension in Eq (18), was introduced on n-dimensional Euclidian space [6] and was subsequently furhter generalized to other functional spaces, namely Hilbert and Banach spaces, and topological groups [46,39,47].…”

Section: Measure On Topological Groupsmentioning

confidence: 99%

Elements of a function analytic approach to probability.

Red-Horse

Ghanem

2008

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We first provide a detailed motivation for using probability theory as a mathematical context in which to analyze engineering and scientific systems that possess uncertainties. We then present introductory notes on the function analytic approach to probabilistic analysis, emphasizing the connections to various classical deterministic mathematical analysis elements. Lastly, we describe how to use the approach as a means to augment deterministic analysis methods in a particular Hilbert space context, and thus enable a rigorous framework for commingling deterministic and probabilistic analysis tools in an application setting.

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Probability Distributions on Topological Groups

Cited by 54 publications

References 31 publications

Analysis on compact Lie groups of large dimension and on connected compact groups

Analysis on compact Lie groups of large dimension and on connected compact groups

Limit theorems in free probability theory II

Elements of a function analytic approach to probability.

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