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Author : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
Page : 576 pages
File Size : 51,6 Mb
Release : 2023-06-06
Category : Mathematics
ISBN : 9783111233871
Author : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
Page : 372 pages
File Size : 49,6 Mb
Release : 2019-05-06
Category : Mathematics
ISBN : 9783110641257
This book discusses almost periodic and almost automorphic solutions to abstract integro-differential Volterra equations that are degenerate in time, and in particular equations whose solutions are governed by (degenerate) solution operator families with removable singularities at zero. It particularly covers abstract fractional equations and inclusions with multivalued linear operators as well as abstract fractional semilinear Cauchy problems.
Author : Gani T. Stamov
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 55,9 Mb
Release : 2012-03-09
Category : Mathematics
ISBN : 9783642275456
In the present book a systematic exposition of the results related to almost periodic solutions of impulsive differential equations is given and the potential for their application is illustrated.
Author : A.M. Fink
Publisher : Springer
Page : 345 pages
File Size : 45,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540383079
Author : Paul H. Bezandry,Toka Diagana
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 44,5 Mb
Release : 2011-04-07
Category : Mathematics
ISBN : 9781441994769
This book lays the foundations for a theory on almost periodic stochastic processes and their applications to various stochastic differential equations, functional differential equations with delay, partial differential equations, and difference equations. It is in part a sequel of authors recent work on almost periodic stochastic difference and differential equations and has the particularity to be the first book that is entirely devoted to almost periodic random processes and their applications. The topics treated in it range from existence, uniqueness, and stability of solutions for abstract stochastic difference and differential equations.
Author : Gaston M. N'Guérékata
Publisher : Springer Nature
Page : 134 pages
File Size : 44,9 Mb
Release : 2021-05-28
Category : Mathematics
ISBN : 9783030737184
This book presents the foundation of the theory of almost automorphic functions in abstract spaces and the theory of almost periodic functions in locally and non-locally convex spaces and their applications in differential equations. Since the publication of Almost automorphic and almost periodic functions in abstract spaces (Kluwer Academic/Plenum, 2001), there has been a surge of interest in the theory of almost automorphic functions and applications to evolution equations. Several generalizations have since been introduced in the literature, including the study of almost automorphic sequences, and the interplay between almost periodicity and almost automorphic has been exposed for the first time in light of operator theory, complex variable functions and harmonic analysis methods. As such, the time has come for a second edition to this work, which was one of the most cited books of the year 2001. This new edition clarifies and improves upon earlier materials, includes many relevant contributions and references in new and generalized concepts and methods, and answers the longtime open problem, "What is the number of almost automorphic functions that are not almost periodic in the sense of Bohr?" Open problems in non-locally convex valued almost periodic and almost automorphic functions are also indicated. As in the first edition, materials are presented in a simplified and rigorous way. Each chapter is concluded with bibliographical notes showing the original sources of the results and further reading.
Author : Toka Diagana
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 48,7 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9783319008493
This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their recent generalizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standard references that currently exist on those new classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basic introductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and/or advanced undergraduate student. Moreover, it will be of a great interest to researchers in mathematics as well as in engineering, in physics, and related areas. Further, some parts of the book may be used for various graduate and undergraduate courses.
Author : Yoshiyuki Hino,Toshiki Naito,Nguyen VanMinh,Jong Son Shin
Publisher : CRC Press
Page : 258 pages
File Size : 54,5 Mb
Release : 2001-10-25
Category : Mathematics
ISBN : 9781482263169
This monograph presents recent developments in spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach Spaces. Many of the results represent significant advances in this area. In particular, the authors systematically present a new approach based on the so-called evolution semigroups with
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 47,7 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814470919
Author : Gaston M. N'Guerekata
Publisher : World Scientific
Page : 219 pages
File Size : 45,7 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812818249
This book presents recent methods of study on the asymptotic behavior of solutions of abstract differential equations such as stability, exponential dichotomy, periodicity, almost periodicity, and almost automorphy of solutions. The chosen methods are described in a way that is suitable to those who have some experience with ordinary differential equations. The book is intended for graduate students and researchers in the related areas.
Author : B. M. Levitan,V. V. Zhikov
Publisher : CUP Archive
Page : 232 pages
File Size : 53,8 Mb
Release : 1982-12-02
Category : Mathematics
ISBN : 0521244072
Author : L. Amerio,G. Prouse
Publisher : Springer Science & Business Media
Page : 191 pages
File Size : 53,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475712544
The theory of almost-periodic functions with complex values, created by H. Bohr [1] in his two classical papers published in Acta Mathematica in 1925 and 1926, has been developed by many authors and has had note worthy applications: we recall the works of Weyl, De la Vallee Poussin, Bochner, Stepanov, Wiener, Besicovic, Favard, Delsarte, Maak, Bogoliu bov, Levitan. This subject has been widely treated in the monographs by Bohr [2], Favard [1], Besicovic [1], Maak [1], Levitan [1], Cinquini [1], Corduneanu [1], [2]. An important class of almost-periodic functions was studied at the beginning of the century by Bohl and Esclangon. Bohr's theory has been extended by Muckenhoupt [1] in a particular case and, subsequently, by Bochner [1] and by Bochner and Von Neumann [1] to very general abstract spaces. The extension to Banach spaces is, in particular, of great interest, in view of the fundamental importance of these spaces in theory and application.
Author : Karl H. Hofmann,Sidney A. Morris
Publisher : Walter de Gruyter GmbH & Co KG
Page : 1076 pages
File Size : 55,7 Mb
Release : 2023-10-23
Category : Mathematics
ISBN : 9783111172606
Author : Zhang Chuanyi
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 42,7 Mb
Release : 2003-06-30
Category : Mathematics
ISBN : 140201158X
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.
Author : Ştefan Ovidiu I. Tohăneanu
Publisher : Walter de Gruyter GmbH & Co KG
Page : 276 pages
File Size : 46,7 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 9783111214795
This book aims to be a comprehensive treatise on the interactions between Coding Theory and Commutative Algebra. With the help of a multitude of examples, it expands and systematizes the known and versatile commutative algebraic framework used, since the early 90’s, to study linear codes. The book provides the necessary background for the reader to advance with similar research on coding theory topics from commutative algebraic perspectives.
