Almost Periodic Type Functions And Ergodicity

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Almost Periodic Type Functions And Ergodicity

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Author : Zhang Chuanyi
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-30

Almost Periodic Type Functions And Ergodicity written by Zhang Chuanyi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-30 with Mathematics categories.

The theory of almost periodic functions was first developed by the Danish mathematician H. Bohr during 1925-1926. Then Bohr's work was substantially extended by S. Bochner, H. Weyl, A. Besicovitch, J. Favard, J. von Neumann, V. V. Stepanov, N. N. Bogolyubov, and oth ers. Generalization of the classical theory of almost periodic functions has been taken in several directions. One direction is the broader study of functions of almost periodic type. Related this is the study of ergodic ity. It shows that the ergodicity plays an important part in the theories of function spectrum, semigroup of bounded linear operators, and dynamical systems. The purpose of this book is to develop a theory of almost pe riodic type functions and ergodicity with applications-in particular, to our interest-in the theory of differential equations, functional differen tial equations and abstract evolution equations. The author selects these topics because there have been many (excellent) books on almost periodic functions and relatively, few books on almost periodic type and ergodicity. The author also wishes to reflect new results in the book during recent years. The book consists of four chapters. In the first chapter, we present a basic theory of four almost periodic type functions. Section 1. 1 is about almost periodic functions. To make the reader easily learn the almost periodicity, we first discuss it in scalar case. After studying a classical theory for this case, we generalize it to finite dimensional vector-valued case, and finally, to Banach-valued (including Hilbert-valued) situation.

Almost Periodic Type Functions And Ergodicity

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Author : Zhang Chuanyi
language : en
Publisher: Springer
Release Date : 2013-09-14

Almost Periodic Type Functions And Ergodicity written by Zhang Chuanyi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-14 with Mathematics categories.

The theory of almost periodic functions was first developed by the Danish mathematician H. Bohr during 1925-1926. Then Bohr's work was substantially extended by S. Bochner, H. Weyl, A. Besicovitch, J. Favard, J. von Neumann, V. V. Stepanov, N. N. Bogolyubov, and oth ers. Generalization of the classical theory of almost periodic functions has been taken in several directions. One direction is the broader study of functions of almost periodic type. Related this is the study of ergodic ity. It shows that the ergodicity plays an important part in the theories of function spectrum, semigroup of bounded linear operators, and dynamical systems. The purpose of this book is to develop a theory of almost pe riodic type functions and ergodicity with applications-in particular, to our interest-in the theory of differential equations, functional differen tial equations and abstract evolution equations. The author selects these topics because there have been many (excellent) books on almost periodic functions and relatively, few books on almost periodic type and ergodicity. The author also wishes to reflect new results in the book during recent years. The book consists of four chapters. In the first chapter, we present a basic theory of four almost periodic type functions. Section 1. 1 is about almost periodic functions. To make the reader easily learn the almost periodicity, we first discuss it in scalar case. After studying a classical theory for this case, we generalize it to finite dimensional vector-valued case, and finally, to Banach-valued (including Hilbert-valued) situation.

Almost Periodic Type Functions And Ergodicity

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Author : Chuanyi Zhang
language : en
Publisher:
Release Date : 2003

Almost Periodic Type Functions And Ergodicity written by Chuanyi Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Almost periodic functions categories.

Nonautonomous Fractional Evolution Equations

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Author : Yong Zhou
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-07-01

Nonautonomous Fractional Evolution Equations written by Yong Zhou and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-01 with Mathematics categories.

Fractional evolution equations describe various complex and nonlocal systems with memory. This volume investigates fractional evolution equations, in infinite intervals. The book covers a range of topics, including the existence, uniqueness, attractivity, and applications to fractional diffusion equations and fractional Schrodinger equations. Researchers and graduate students in pure and applied mathematics will find this a useful reference.

Selected Topics In Almost Periodicity

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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-22

Selected Topics In Almost Periodicity written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.

Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.

Harmonic Limits Of Dynamical And Control Systems

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Author : Tobias Wichtrey
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2011

Harmonic Limits Of Dynamical And Control Systems written by Tobias Wichtrey and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

In this thesis, we will analyze an approach to describe the rotational behaviour of dynamical systems and control systems, namely the concept of rotational factor maps. The general idea is to find a complex-valued map F on the state space that maps the dynamics onto a rotation around the origin in the complex plane. We will call such a map a rotational factor map. More formally, these rotational factor maps are eigenfunctions of the Koopman operator. This concept of rotational factor maps is closely connected to harmonic limits, which are ergodic sums (for discrete-time systems) or integrals (for systems in continuous time). It turns out that the existence of rotational factor maps is equivalent to the existence of non-zero harmonic limits. So we use harmonic limits to analyse the spectral properties of dynamical systems given by the iteration of a map, by a semi-flow or by a control system.

Levy Processes Integral Equations Statistical Physics Connections And Interactions

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Author : Lev A. Sakhnovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-18

Levy Processes Integral Equations Statistical Physics Connections And Interactions written by Lev A. Sakhnovich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-18 with Mathematics categories.

In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis also plays a central role in the present book. However, our approach is mainly based on the application of analysis methods (the method of operator identities, integral equations theory, dual systems, integrable equations) to probability theory (Levy processes, M. Kac's problems, the principle of imperceptibility of the boundary, signal theory). The essential part of the book is dedicated to problems of statistical physics (classical and quantum cases). We consider the corresponding statistical problems (Gibbs-type formulas, non-extensive statistical mechanics, Boltzmann equation) from the game point of view (the game between energy and entropy). One chapter is dedicated to the construction of special examples instead of existence theorems (D. Larson's theorem, Ringrose's hypothesis, the Kadison-Singer and Gohberg-Krein questions). We also investigate the Bezoutiant operator. In this context, we do not make the assumption that the Bezoutiant operator is normally solvable, allowing us to investigate the special classes of the entire functions.

Advances In Interdisciplinary Mathematical Research

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Author : Bourama Toni
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-07-08

Advances In Interdisciplinary Mathematical Research written by Bourama Toni and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Mathematics categories.

This volume contains the invited contributions to the Spring 2012 seminar series at Virginia State University on Mathematical Sciences and Applications. It is a thematic continuation of work presented in Volume 24 of the Springer Proceedings in Mathematics & Statistics series. Contributors present their own work as leading researchers to advance their specific fields and induce a genuine interdisciplinary interaction. Thus all articles therein are selective, self-contained, and are pedagogically exposed to foster student interest in science, technology, engineering and mathematics, stimulate graduate and undergraduate research, as well as collaboration between researchers from different areas. The volume features new advances in mathematical research and its applications: anti-periodicity; almost stochastic difference equations; absolute and conditional stability in delayed equations; gamma-convergence and applications to block copolymer morphology; the dynamics of collision and near-collision in celestial mechanics; almost and pseudo-almost limit cycles; rainbows in spheres and connections to ray, wave and potential scattering theory; null-controllability of the heat equation with constraints; optimal control for systems subjected to null-controllability; the Galerkin method for heat transfer in closed channels; wavelet transforms for real-time noise cancellation; signal, image processing and machine learning in medicine and biology; methodology for research on durability, reliability, damage tolerance of aerospace materials and structures at NASA Langley Research Center. The volume is suitable and valuable for mathematicians, scientists and research students in a variety of interdisciplinary fields, namely physical and life sciences, engineering and technology including structures and materials sciences, computer science for signal, image processing and machine learning in medicine.

Dynamic Equations On Time Scales And Applications

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Author : Ravi P Agarwal
language : en
Publisher: CRC Press
Release Date : 2024-10-18

Dynamic Equations On Time Scales And Applications written by Ravi P Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-18 with Mathematics categories.

This book presents the theory of dynamic equations on time scales and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results related to the qualitative properties of solutions like existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. Presents cutting-edge research trends of dynamic equations and recent advances in contemporary research on the topic of time scales Connects several new areas of dynamic equations on time scales with applications in different fields Includes mathematical explanation from the perspective of existing knowledge of dynamic equations on time scales Offers several new recently developed results, which are useful for the mathematical modeling of various phenomena Useful for several interdisciplinary fields like economics, biology, and population dynamics from the perspective of new trends The text is for postgraduate students, professionals, and academic researchers working in the fields of Applied Mathematics

Ergodic Theory

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Author : David Kerr
language : en
Publisher: Springer
Release Date : 2017-02-09

Ergodic Theory written by David Kerr and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-09 with Mathematics categories.

This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy. The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.