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WAVE EQUATION AND MULTIPLIER ESTIMATES ON DAMEK–RICCI SPACES
, 806
"... Abstract. Let S be a Damek–Ricci space and L be a distinguished left invariant Laplacian on S. We prove pointwise estimates for the convolution kernels of spectrally localized wave operators of the form e it √ L ψ ..."
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Abstract. Let S be a Damek–Ricci space and L be a distinguished left invariant Laplacian on S. We prove pointwise estimates for the convolution kernels of spectrally localized wave operators of the form e it √ L ψ
Brownian motion on Lie groups and open quantum systems
 J. Phys. A: Math. Theor
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Subordinated multiparameter groups of linear operators: Properties via the transference principle
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Convolution hemigroups of bounded variation on a Lie projective group
"... In a previous article [11] we studied the central limit theorem for innitesimal triangular arrays of probability measures on a Lie group. Since the work [2] of Berg and more recently of Bendikov [1] similar studies appeared to be urgent for the innite{dimensional torus group and beyond that for the ..."
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In a previous article [11] we studied the central limit theorem for innitesimal triangular arrays of probability measures on a Lie group. Since the work [2] of Berg and more recently of Bendikov [1] similar studies appeared to be urgent for the innite{dimensional torus group and beyond that for the class of Lie projective groups which among others contains
Random walks on Lie groups
"... The goal of these notes is to give an introduction to random walks and limit theorems on Lie groups, mostly amenable Lie groups, with an emphasis on equidistribution problems. We also state a number of open problems. In Section 1 we define the basic notions regarding probability measures on groups, ..."
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The goal of these notes is to give an introduction to random walks and limit theorems on Lie groups, mostly amenable Lie groups, with an emphasis on equidistribution problems. We also state a number of open problems. In Section 1 we define the basic notions regarding probability measures on groups, convergence in distribution, recurrence, equidistribution, Brownian motions, limit theorems, etc. Most notably we state and prove the Central Limit Theorem on Lie groups. Oddly enough, the proof of this fundamental theorem cannot be found in the literature in a simple and complete form, although it was established almost 45 years ago by Wehn. The exposition here will I hope make up for that. In Section 2 we discuss the equidistribution properties of random walks in Lie groups and survey the existing ratio limit theorems and local limit theorems in this context. We give several examples including the ItôKawada equidistribution theorem for compact groups and the local limit theorem for random walks by isometries on the plane, of which we give a full proof thus generalizing an old theorem of Kazhdan. In Section 3 we study in more detail the case of nilpotent Lie groups, rephrase the
ON THE REGULARITY OF SAMPLE PATHS OF SUBELLIPTIC DIFFUSIONS ON MANIFOLDS
, 2004
"... Using heat kernel Gaussian estimates and related properties, we study the intrinsic regularity of the sample paths of the Hunt process associated to a strictly local regular Dirichlet form. We describe how the results specialize to Riemannian Brownian motion and to subelliptic symmetric diffusions. ..."
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Using heat kernel Gaussian estimates and related properties, we study the intrinsic regularity of the sample paths of the Hunt process associated to a strictly local regular Dirichlet form. We describe how the results specialize to Riemannian Brownian motion and to subelliptic symmetric diffusions. 1.
LÉVY PROCESSES AND THEIR SUBORDINATION IN MATRIX LIE GROUPS
"... Abstract. Lévy processes in matrix Lie groups are studied. Subordination (random time change) is used to show that quasiinvariance of the Brownian motion in a Lie group induces absolute continuity of the laws of the corresponding pure jump processes. These results are applied to several examples wh ..."
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Abstract. Lévy processes in matrix Lie groups are studied. Subordination (random time change) is used to show that quasiinvariance of the Brownian motion in a Lie group induces absolute continuity of the laws of the corresponding pure jump processes. These results are applied to several examples which are discussed in detail. Table of Contents