Currently displaying 1 – 20 of 22

Showing per page

Order by Relevance | Title | Year of publication

What can we do to support the applied mathematics in Poland?

Ewa Damek — 2014

Mathematica Applicanda

In the past two years I talked to a great many people. One of the fundamental questions concerning the further development of applied mathematics in Poland is whether to appoint a new discipline (s) in the field of mathematics or not. Such a possible new discipline could be, for example. Applied statistics and mathematics calculation. Opinions are divided. The basic argument is this: ”If you summon a new discipline, it will give an impulse to the development of this kind of research in Poland. It...

Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group

Ewa DamekAndrzej Hulanicki — 1991

Studia Mathematica

On the domain S_a = {(x,e^b): x ∈ N, b ∈ ℝ, b > a} where N is a simply connected nilpotent Lie group, a certain N-left-invariant, second order, degenerate elliptic operator L is considered. N × {e^a} is the Poisson boundary for L-harmonic functions F, i.e. F is the Poisson integral F(xe^b) = ʃ_N f(xy)dμ^b_a(x), for an f in L^∞(N). The main theorem of the paper asserts that the maximal function M^a f(x) = sup{|ʃf(xy)dμ_a^b(y)| : b > a} is of weak type (1,1).

Asymptotic behavior of the invariant measure for a diffusion related to an NA group

Ewa DamekAndrzej Hulanicki — 2006

Colloquium Mathematicae

On a Lie group NA that is a split extension of a nilpotent Lie group N by a one-parameter group of automorphisms A, the heat semigroup μ t generated by a second order subelliptic left-invariant operator j = 0 m Y j + Y is considered. Under natural conditions there is a μ ̌ t -invariant measure m on N, i.e. μ ̌ t * m = m . Precise asymptotics of m at infinity is given for a large class of operators with Y₀,...,Yₘ generating the Lie algebra of S.

Regular behavior at infinity of stationary measures of stochastic recursion on NA groups

Dariusz BuraczewskiEwa Damek — 2010

Colloquium Mathematicae

Let N be a simply connected nilpotent Lie group and let S = N ( ) d be a semidirect product, ( ) d acting on N by diagonal automorphisms. Let (Qₙ,Mₙ) be a sequence of i.i.d. random variables with values in S. Under natural conditions, including contractivity in the mean, there is a unique stationary measure ν on N for the Markov process Xₙ = MₙXn-1 + Qₙ. We prove that for an appropriate homogeneous norm on N there is χ₀ such that l i m t t χ ν x : | x | > t = C > 0 . In particular, this applies to classical Poisson kernels on symmetric spaces,...

Hua-harmonic functions on symmetric type two Siegel domains

Dariusz BuraczewskiEwa Damek — 2002

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study a natural system of second order differential operators on a symmetric Siegel domain D that is invariant under the action of biholomorphic transformations. If D is of type two, the space of real valued solutions coincides with pluriharmonic functions. We show the main idea of the proof and give a survey of previous results.

On the invariant measure of the random difference equation Xn = AnXn−1 + Bn in the critical case

Sara BrofferioDariusz BuraczewskiEwa Damek — 2012

Annales de l'I.H.P. Probabilités et statistiques

We consider the autoregressive model on ℝ defined by the stochastic recursion = −1 + , where {( , )} are i.i.d. random variables valued in ℝ× ℝ+. The critical case, when 𝔼 [ log A 1 ] = 0 , was studied by Babillot, Bougerol and Elie, who proved that there exists a unique invariant Radon measure for the Markov chain { }. In the present paper we prove that the weak limit of properly dilated...

Page 1 Next

Download Results (CSV)