dc.contributor.author | Alexopoulos, Georgios K. | en |
dc.creator | Alexopoulos, Georgios K. | en |
dc.date.accessioned | 2019-12-02T10:33:29Z | |
dc.date.available | 2019-12-02T10:33:29Z | |
dc.date.issued | 2002 | |
dc.identifier.uri | http://gnosis.library.ucy.ac.cy/handle/7/56389 | |
dc.description.abstract | We 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.source | Probability Theory and Related Fields | en |
dc.source.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-0036026172&doi=10.1007%2fs004400200212&partnerID=40&md5=ed7cbded2014b8b6e275fde75aa2616a | |
dc.subject | Convolution | en |
dc.subject | Central limit theorem | en |
dc.subject | Density | en |
dc.subject | Harnack inequality | en |
dc.subject | Heat kernel | en |
dc.subject | Lie group | en |
dc.title | Centered densities on Lie groups of polynomial volume growth | en |
dc.type | info:eu-repo/semantics/article | |
dc.identifier.doi | 10.1007/s004400200212 | |
dc.description.volume | 124 | |
dc.description.issue | 1 | |
dc.description.startingpage | 112 | |
dc.description.endingpage | 150 | |
dc.author.faculty | Σχολή Θετικών και Εφαρμοσμένων Επιστημών / Faculty of Pure and Applied Sciences | |
dc.author.department | Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics | |
dc.type.uhtype | Article | en |
dc.description.notes | <p>Cited By :8</p> | en |
dc.source.abbreviation | Probab.Theory Relat.Fields | en |