Browsing by Author "Alexopoulos, Georgios K."
Now showing items 113 of 13

Article
An application of homogenization theory to harmonic analysis on solvable lie groups of polynomial growth
Alexopoulos, Georgios K. (1993)Let Q be a connected solvable Lie group of polynomial growth. Let also E1, …, Ep be left invariant vector fields on G that satisfy Hοrmander’s condition and denote by L = (E1 2 +… + Ep 2) the associated subLaplacian and ...

Article
Centered densities on Lie groups of polynomial volume growth
Alexopoulos, Georgios K. (2002)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 ...

Article
Centered subLaplacians and densities in Lie groups of polynomial volume growth
Alexopoulos, Georgios K. (1998)We prove a Harnack inequality on connected Lie groups of polynomial volume growth. We use this inequality to study the large time behavior of the heat kernels associated to centered subLaplacians. Thus, we obtain Gaussian ...

Article
Convolution powers on groups of polynomial volume growth
Alexopoulos, Georgios K. (1997)We give certain estimates concerning the asymptotic behavior of convolution powers of measures on discrete groups and connected Lie groups of polynomial volume growth. We also give similar estimates for the heat kernels ...

Article
On the large time behavior of heat kernels on Lie groups
Lohoué, N.; Alexopoulos, Georgios K. (2003)We prove Gaussian estimates for heat kernels on semisimple Lie groups by using the method of Block wave representation. We also give a large time asymptotic expansion for heat kernels on compact extensions of abelian Lie groups.

Article
On the large time behavior of the heat kernels of quasiperiodic differential operators
Alexopoulos, Georgios K. (2000)We prove an analog of the BerryEsseen estimate for the heat kernel of second order elliptic differential operators with quasiperiodic coefficients. As an application of this result, we prove the Lp boundedness of the ...

Article
Oscillating Multipliers on Lie Groups and Riemannian Manifolds
Alexopoulos, Georgios K. (1994)We prove Lpestimates for oscillating spectral multipliers on Lie groups of polynomial volume growth and Riemannian manifolds of nonnegative curvature. We apply these results to obtain Lpestimates for the Riesz means of the ...

Article
Random walks on discrete groups of polynomial volume growth
Alexopoulos, Georgios K. (2002)Let μ be a probability measure with finite support on a discrete group Γ of polynomial volume growth. The main purpose of this paper is to study the asymptotic behavior of the convolution powers μ*n μ. If μ is centered, ...

Article
Sobolev Inequalities and Harmonic Functions of Polynomial Growth
Alexopoulos, Georgios K.; Lohoué, N. (1993)We prove a Sobolev inequality for functions not necessarily with compact support, on a connected Lie group G of polynomial volume growth. To prove this inequality we have to characterise the harmonic functions of polynomial ...

Article
Spectral multipliers for Markov chains
Alexopoulos, Georgios K. (2004)We prove an analog to the classical MikhlinHörmander multiplier theorem for Markov chains.

Article
Spectral multipliers on discrete groups
Alexopoulos, Georgios K. (2001)The classical MikhlinHörmander multiplier theorem is generalised to the context of discrete groups of polynomial volume growth.

Article
Spectral multipliers on lie groups of polynomial growth
Alexopoulos, Georgios K. (1994)Let L be a left invariant subLaplacian on a connected Lie group G of polynomial volume growth, and let (Eγγ ≥ 0) be the spectral resolution of L and m a bounded Borel measurable function on [0, ∞). In this article we give ...

Article
SubLaplacians with drift on Lie groups of polynomial volume growth
Alexopoulos, Georgios K. (2002)We prove a parabolic Harnack inequality for a centered subLaplacian L on a connected Lie group G of polynomial volume growth by using ideas from Homogenisation theory and by adapting the method of Krylov and Safonov. We ...