L\u3csup\u3ep\u3c/sup\u3e Estimates for the Maximal Functions

This talk was given during the Jozef Marcinkiewicz Centenary Conference

Weak Type Inequalities for Maximal Operators Associated to Double Ergodic Sums

Given an approach region Γ ∈ Z+2 and a pair U, V of commuting nonperiodic measure preserving transformations on a probability space (Ω, Σ, μ), it is shown that either the associated multiparameter ergodic averages of any function in L1(Ω) converge a.e. or that, given a positive increasing function ϕ on [0,∞) that is o(log x) as x → ∞, there exists a function g ∈ Lϕ(L)(Ω) whose associated multiparameter ergodic averages fail to converge a.e

On the Generalized Linear and Non-Linear DFC in Non-Linear Dynamics

The article is devoted to investigation of robust stability of the generalized linear control of the discrete autonomous dynamical systems. Sharp necessary conditions on the size of the set of multipliers that guaranty robust stabilization of the equilibrium of the system are provided. Surprisingly enough it turns out that the generalized linear delayed feedback control has same limitation as the classical Pyragas DFC. This generalized Ushio 1996 DFC limitation statement. Note that in scalar case a generalized non-linear control can robustly stabilize an equilibrium for any admissible range of multipliers. In the current article similar result is obtained in the vector-valued setting

From Chaos to Order Through Mixing

In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach allows us to locally stabilize a priori unknown cycles of a given length. As a special case, we have a cycle stabilization using nonlinear feedback. Several examples are considered

Moduli of smoothness and rate of a.e. convergence for some convolution operators

Vegeu el resum a l'inici del document del fitxer adjunt

On Maximal Operators Associated to Bases of Some Convex Sets

It will be shown that a differentiation basis associated to a dilation and translation invariant basis of some multidimensional convex sets if differentiate integral of any functioin from L^∞ must differentiate integral of any function from L^p with some

On the Rate of a.e. Convergence by Convolution Type Means

The talk is based on joint work with Walter Trebels (TU Darmstadt). K.I. Oskolkov 1977 raised the problem, how the norm-smoothness of f(x) entails a certain rate of a.e. convergence of an approximation process Ttf(x) towards f(x) for t → 0+ . The purpose of this talk is to demonstrate nearly optimal results concerning the rate of almost everywhere convergence of the Gauss-Weierstrass, Abel-Poisson, and Bochner-Riesz means of the one-dimensional Fourier integral. A typical result for these means is the following: If the function f belongs to the Besov space Bs p,p, 1 \u3c p \u3c ∞, 0 \u3c s \u3c 1, then Tmtf(x) − f(x) = ox(ts) a.e. as t → 0 +

On Multidimensional Extension of Dini Test

An anisotropic multidimensional version of Dini test will be presented

Fourier Analysis and Nonlinear Dynamics

I will show some applications of classical Fourier analysis to the problems of discrete nonlinear dynamics. This is a joint talk with D. Dmitrishin, A. Khamitova and A. Solyanik

On Chaos Stabilization in Nonlinear Autonomous Discrete Dynamical Systems

We propose an optimal average coeÿcients to stabilize equilibrium of nonlin-ear autonomous discrete dynamical systems. This is a joint talk with D.Dmitrishin and A.Khamitova