SelectedWorks - Alexander M. Stokolos

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Selected Works of Alexander M. Stokolos

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Research Interests: My scientific interest is in Harmonic and Computation Analysis, Ergodic Theory, Boundary Behavior of Solutions of Elliptic PDE and Analytic Functions, Direct and Converse Theorems of Constructive Approximation Theory, Metric Number Theory, Nonlinear Dynamics and the Bellman Functions Method

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About Alexander M. Stokolos

Research Interests: My scientific interest is in Harmonic and Computation Analysis, Ergodic Theory, Boundary Behavior of Solutions of Elliptic PDE and Analytic Functions, Direct and Converse Theorems of Constructive Approximation Theory, Metric Number Theory, Nonlinear Dynamics and the Bellman Functions Method

Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and ...

Department of Mathematical Sciences Faculty Bookshelf (2017)

Maria Cristina Pereyra, Stefania Marcantognini, Alexander M. Stokolos and Wilfredo Urbina Romero

Book Summary: This book is the second of a two volume series. Covering a range of subjects from operator theory ...

Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and ...

Department of Mathematical Sciences Faculty Bookshelf (2016)

Maria Cristina Pereyra, Stefania Marcantognini, Alexander M. Stokolos and Wilfredo Urbina Romero

Book Summary: Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book ...

Special Functions, Partial Differential Equations, and Harmonic Analysis: In Honor ...

Springer Proceedings in Mathematics and Statistics (2014)

Constantine Georgakis, Alexander M. Stokolos and Wilfredo Urbina

Georgia Southern faculty member Alexander Stokolos co-edited Special Functions, Partial Differential Equations, and Harmonic Analysis: In Honor of Calixto P. ...

Recent Advances in Harmonic Analysis and Applications: In Honor of ...

Laura De Carli, Dmitriy Bilyk, Alexander Petukhov, Alexander M. Stokolos, et al.

Georgia Southern faculty member Alexander Stokolos co-edited Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov in ...

Topics in Harmonic Analysis and Ergodic Theory

Joseph M. Rosenblatt, Alexander M. Stokolos and Ahmed I. Zayed

Prior to starting his position at Georgia Southern University, Georgia Southern faculty member Alexander Stokolos co-edited Comptemporary Mathematics: Topics in ...

Submitted Articles (5)

Fast Cycles Detecting in Non-Linear Discrete Systems

arXiv Repository (2016)

Dmitriy Dmitrishin, Elena Franzheva and Alexander M. Stokolos

In the paper below we consider a problem of stabilization of a priori unknown unstable periodic orbits in non-linear autonomous ...

From Chaos to Order Through Mixing

arXiv Repository (2016)

Dmitriy Dmitrishin, I. M. Skrinnik and Alexander M. Stokolos

In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control ...

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

arXiv Repository (2015)

Dmitriy Dmitrishin, Anna Khamitova and Alexander M. Stokolos

The article is devoted to investigation of robust stability of the generalized linear control of the discrete autonomous dynamical systems. ...

Fejér and Suffridge Polynomials in the Delayed Feedback Control Theory

arXiv Repository (2014)

Dmitriy Dmitrishin, Anna Khamitova, Anatolii Korenovskyi and Alexander M. Stokolos

A remarkable connection between optimal delayed feedback control (DFC) and complex polynomial mappings of the unit disc is established. The ...

Fejér Polynomials and Control of Nonlinear Discrete Systems

Preprint (2010)

Dmitriy Dmitrishin, Paul Hagelstein, Anna Khamitova, Anatolii Korenovskyi, et al.

We consider optimization problems associated to a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time ...

On the Stability of Cycles by Delayed Feedback Control

Linear and Multilinear Algebra (2015)

Dmitriy Dmitrishin, Paul Hagelstein, Anna Khamitova and Alexander M. Stokolos

We present a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we ...

Contribution to Book

Fejér Polynomials and Chaos

Special Functions, Partial Differential Equations, and Harmonic Analysis: In Honor of Calixto P. Calderón (2014)

Dmitriy Dmitrishin, Anna Khamitova and Alexander M. Stokolos

We show that given any μ > 1, an equilibrium x of a dynamic system xn+1=f(xn) (1) can be robustly ...

Contribution to Book

Moduli of Smoothness and Rate of a.e. Convergence for ...

Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov (2013)

Alexander M. Stokolos and Walter Trebels

One purpose of this chapter is to establish results on the rate of almost everywhere convergence of approximation processes of ...

Contribution to Book

On the Scientific Work of Konstantin Ilyich Oskolkov

Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov (2013)

Dmitriy Bilyk, Laura De Carli, Alexander Petukhov, Alexander M. Stokolos, et al.

This chapter is a brief account of the life and the scientific work of K.I. Oskolkov.

Contribution to Book

Some Applications of Equimeasurable Rearrangements

Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov (2013)

Anatolii A. Korenovskii and Alexander M. Stokolos

The goal of this chapter is to demonstrate the utility of equimeasurable rearrangements in studying certain function classes.

Transference of Weak Type Bounds of Multiparameter Ergodic and Geometric ...

Fundamenta Mathematicae (2012)

Paul Hagelstein and Alexander M. Stokolos

Let U1,…,Ud be a non-periodic collection of commuting measure preserving transformations on a probability space (Ω,Σ,μ). Also let Γ be ...

Weak Type Inequalities for Maximal Operators Associated to Double Ergodic ...

New York Journal of Mathematics (2011)

Paul Hagelstein and Alexander M. Stokolos

Given an approach region Γ ∈ Z+2 and a pair U, V of commuting nonperiodic measure preserving transformations on a ...

Weak Type Inequalities for Ergodic Strong Maximal Operators

Acta Scientiarum Mathematicarum (2010)

Paul Hagelstein and Alexander M. Stokolos

Fava's weak type LlogL estimate for strong two-parameter ergodic maximal operators associated to pairs of commuting non-periodic measure-preserving transformations is ...

Tauberian Conditions for Geometric Maximal Operators

Transactions of the American Mathematical Society (2009)

Paul Hagelstein and Alexander M. Stokolos

Let B be a collection of measurable sets in Rn. The associated geometric maximal operator MB is defined on L1(Rn) ...

An Extension of the Córdoba–Fefferman Theorem on the Equivalence ...

Comptes Rendus Mathematique (2008)

Paul Hagelstein and Alexander M. Stokolos

The Córdoba–Fefferman theorem involving the equivalence between boundedness properties of certain classes of maximal and multiplier operators is extended utilizing ...

Properties of the Maximal Functions Associated to Bases of Rectangles ...

Proceedings of Edinburgh Mathematical Society (2008)

Alexander M. Stokolos

This paper is an attempt to understand a phenomenon of maximal operators associated with bases of three-This paper is an ...

Monge-Ampère Equations and Bellman Functions: The Dyadic Maximal Operator

Comptes Rendus Mathematique (2008)

Leonid Slavin, Alexander M. Stokolos and Vasily Vasyunin

We find explicitly the Bellman function for the dyadic maximal operator on Lp as the solution of a Bellman partial ...

A Note on the Maximal Gurov-Reshetnyak Condition

Annales Academiæ Scientiarum Fennicæ (2007)

A. A. Korenovskyy, A. K. Lerner and Alexander M. Stokolos

In a recent paper [17] we established an equivalence between the Gurov–Reshetnyak and A∞ conditions for arbitrary absolutely continuous measures. ...

On Weak Type Inequalities for Rare Maximal Functions in ℝⁿ

Colloquium Mathematicum (2006)

Alexander M. Stokolos

The study of one-dimensional rare maximal functions was started in [5, 4]. The main result in [5] was obtained with ...

On the Sharpness of the Stolz Approach

Annales Academiæ Scientiarum Fennicæ (2006)

Fausto Di Biase, Alexander M. Stokolos, Olof Svensson and Tomasz Weiss

We study the sharpness of the Stolz approach for the a.e. convergence of functions in the Hardy spaces in the ...