Some remarks on the random walk on finite groups
Corrigendum to "On density modulo 1 of some expressions containing algebraic integers" (Acta Arith. 127 (2007), 217-229)
Sequences of algebraic integers and density modulo
We prove density modulo of the sets of the form where is a pair of rationally independent algebraic integers of degree satisfying some additional assumptions, and is any sequence of real numbers.
On density modulo 1 of some expressions containing algebraic integers
Noncoercive differential operators on homogeneous manifolds of negative curvature and their Green functions
We obtain upper and lower estimates for the Green function for a second order noncoercive differential operator on a homogeneous manifold of negative curvature.
Equidistribution in the dual group of the -adic integers
Let be the quotient group of the -adele ring of an algebraic number field by the discrete group of -integers. Given a probability measure on and an endomorphism of , we consider the relation between uniform distribution of the sequence for -almost all and the behavior of relative to the translations by some rational subgroups of . The main result of this note is an extension of the corresponding result for the -dimensional torus due to B. Host.
A survey of results on density modulo of double sequences containing algebraic numbers
In this survey article we start from the famous Furstenberg theorem on non-lacunary semigroups of integers, and next we present its generalizations and some related results.
Estimates for the Poisson kernel on higher rank NA groups
We obtain an estimate for the Poisson kernel for the class of second order left-invariant differential operators on higher rank NA groups.
Unbounded harmonic functions on homogeneous manifolds of negative curvature
We study unbounded harmonic functions for a second order differential operator on a homogeneous manifold of negative curvature which is a semidirect product of a nilpotent Lie group N and A = ℝ⁺. We prove that if F is harmonic and satisfies some growth condition then F has an asymptotic expansion as a → 0 with coefficients from 𝓓'(N). Then we single out a set of at most two of these coefficients which determine F. Then using asymptotic expansions we are able to prove some theorems...
Corrigendum to the paper "Semigroup actions on tori and stationary measures on projective spaces" (Studia Math. 171 (2005), 33-66)
The evolution and Poisson kernels on nilpotent meta-abelian groups
Let S be a semidirect product S = N⋊ A where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic to , k>1. We consider a class of second order left-invariant differential operators on S of the form , where , and for each is left-invariant second order differential operator on N and , where Δ is the usual Laplacian on . Using some probabilistic techniques (e.g., skew-product formulas for diffusions on S and N respectively) we obtain an...
Semigroup actions on tori and stationary measures on projective spaces
Let Γ be a subsemigroup of G = GL(d,ℝ), d > 1. We assume that the action of Γ on is strongly irreducible and that Γ contains a proximal and quasi-expanding element. We describe contraction properties of the dynamics of Γ on at infinity. This amounts to the consideration of the action of Γ on some compact homogeneous spaces of G, which are extensions of the projective space . In the case where Γ is a subsemigroup of GL(d,ℝ) ∩ M(d,ℤ) and Γ has the above properties, we deduce that the Γ-orbits...
Martin boundary for homogeneous riemannian manifolds of negative curvature at the bottom of the spectrum.
In this paper we treat noncoercive operators on simply connected manifolds of negative curvature.
Estimates for derivatives of the Green functions for the noncoercive differential operators on homogeneous manifolds of negative curvature. II.
Estimates for the mixed derivatives of the Green functions on homogeneous manifolds of negative curvature.
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