Central Gaussian Convolution Semigroups on Compact Groups: A Survey

Bendikov, Alexander; SALOFF-COSTEy, L.

doi:10.1142/s0219025703001456

Cited by 8 publications

(7 citation statements)

References 35 publications

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“…See [6,8,9,11]. It is worth emphasizing the relevance of Conjecture 1 for the problem considered in this section.…”

Section: Easy Results For Productsmentioning

confidence: 99%

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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“…See [6,8,9,11]. It is worth emphasizing the relevance of Conjecture 1 for the problem considered in this section.…”

Section: Easy Results For Productsmentioning

confidence: 99%

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

Saloff‐Coste

2010

Colloq. Math.

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“…This section contains a minimal introduction to the setting of our study. For more details, see [3,5,8] and the references therein.…”

Section: Setting and Notationmentioning

confidence: 99%

Perturbation results concerning Gaussian estimates and hypoellipticity for left-invariant Laplacians on compact groups

Hou¹,

Saloff‐Coste²

2021

Preprint

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In this paper we study left-invariant Laplacians on compact connected groups that are form-comparable perturbations of bi-invariant Laplacians. Our results show that Gaussian bounds for derivatives of heat kernels enjoyed by certain bi-invariant Laplacians hold for their form-comparable perturbations. We further show that the parabolic operators associated with such left-invariant Laplacians, in particular, with the bi-invariant Laplacians, are hypoelliptic in various senses.

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“…For instance, A might be the circle group and Z 0 the p-adic solenoid, see [9, p. 488-489] and [5,6]. 1.…”

Section: Compact Groups With Finite Dimensional Abelian Partmentioning

confidence: 99%

“…A measure µ is central if and only if µ(gV g −1 ) = µ(V ) for each g ∈ G and each Borel set V in G. That is, µ is central if and only if it is invariant under all inner automorphisms of G. A convolution semigroup (µ t ) t>0 is central if and only if µ t is central for each t > 0. For surveys of recent results, see [5,6]. For surveys of recent results, see [5,6].…”

Section: Introductionmentioning

confidence: 99%

Some dichotomy results for central Gaussian convolution semigroups on compact groups

Bendikov

Saloff‐Coste

2002

Probab Theory Relat Fields

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Central Gaussian Convolution Semigroups on Compact Groups: A Survey

Cited by 8 publications

References 35 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

Perturbation results concerning Gaussian estimates and hypoellipticity for left-invariant Laplacians on compact groups

Some dichotomy results for central Gaussian convolution semigroups on compact groups

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