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dc.contributor.authorAlexopoulos, Georgios K.en
dc.creatorAlexopoulos, Georgios K.en
dc.date.accessioned2019-12-02T10:33:29Z
dc.date.available2019-12-02T10:33:29Z
dc.date.issued2002
dc.identifier.urihttp://gnosis.library.ucy.ac.cy/handle/7/56389
dc.description.abstractWe study the asymptotic behavior of the convolution powers φ*n =φ*φ*⋯φ* of a centered density φ on a connected Lie group G of polynomial volume growth. The main tool is a Harnack inequality which is proved by using ideas from Homogenization theory and by adapting the method of Krylov and Safonov. Applying this inequality we prove that the positive φ-harmonic functions are constant. We also characterise the φ-harmonic functions which grow polynomially. We give Gaussian estimates for φ*n as well as for the differences ∂zφ*n(g) = φ*n (gz) - φ*n (g) and ∂1φ*n = φ*n+1 - φ*n. We give estimates, similar to the ones given by the classical Berry-Esseen theorem, for φ*n and ∂z φ*n. We use these estimates to study the associated Riesz transforms.en
dc.sourceProbability Theory and Related Fieldsen
dc.source.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-0036026172&doi=10.1007%2fs004400200212&partnerID=40&md5=ed7cbded2014b8b6e275fde75aa2616a
dc.subjectConvolutionen
dc.subjectCentral limit theoremen
dc.subjectDensityen
dc.subjectHarnack inequalityen
dc.subjectHeat kernelen
dc.subjectLie groupen
dc.titleCentered densities on Lie groups of polynomial volume growthen
dc.typeinfo:eu-repo/semantics/article
dc.identifier.doi10.1007/s004400200212
dc.description.volume124
dc.description.issue1
dc.description.startingpage112
dc.description.endingpage150
dc.author.facultyΣχολή Θετικών και Εφαρμοσμένων Επιστημών / Faculty of Pure and Applied Sciences
dc.author.departmentΤμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics
dc.type.uhtypeArticleen
dc.description.notes<p>Cited By :8</p>en
dc.source.abbreviationProbab.Theory Relat.Fieldsen


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