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Author : Toka Diagana
Publisher : Nova Publishers
ISBN 13 : 9781600216374
Total Pages : 152 pages
Book Rating : 4.74/5 ( download)
Download or read book Pseudo Almost Periodic Functions in Banach Spaces written by Toka Diagana and published by Nova Publishers. This book was released on 2007 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Toka Diagana
Publisher : Springer Science & Business Media
ISBN 13 : 3319008498
Total Pages : 312 pages
Book Rating : 4.93/5 ( download)
Download or read book Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces written by Toka Diagana and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : L. Amerio
Publisher : Springer Science & Business Media
ISBN 13 : 1475712545
Total Pages : 191 pages
Book Rating : 4.44/5 ( download)
Download or read book Almost-Periodic Functions and Functional Equations written by L. Amerio and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Gaston M. N'Guérékata
Publisher : Springer Nature
ISBN 13 : 3030737187
Total Pages : 134 pages
Book Rating : 4.84/5 ( download)
Download or read book Almost Periodic and Almost Automorphic Functions in Abstract Spaces written by Gaston M. N'Guérékata and published by Springer Nature. This book was released on 2021-05-28 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Zhang Chuanyi
Publisher : Springer Science & Business Media
ISBN 13 : 9781402011580
Total Pages : 372 pages
Book Rating : 4.8X/5 ( download)
Download or read book Almost Periodic Type Functions and Ergodicity written by Zhang Chuanyi and published by Springer Science & Business Media. This book was released on 2003-06-30 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110641852
Total Pages : 372 pages
Book Rating : 4.51/5 ( download)
Download or read book Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations written by Marko Kostić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-05-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111234177
Total Pages : 561 pages
Book Rating : 4.75/5 ( download)
Download or read book Metrical Almost Periodicity and Applications to Integro-Differential Equations written by Marko Kostić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-06-06 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of almost periodic functions is a very active field of research for scholars. This research monograph analyzes various classes of multi-dimensional metrically almost periodic type functions with values in complex Banach spaces. We provide many applications of our theoretical results to the abstract Volterra integro-differential inclusions in Banach spaces.
Author : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110763605
Total Pages : 606 pages
Book Rating : 4.07/5 ( download)
Download or read book Selected Topics in Almost Periodicity written by Marko Kostić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-22 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Gaston M. N'Guérékata
Publisher : Springer Science & Business Media
ISBN 13 : 147574482X
Total Pages : 143 pages
Book Rating : 4.28/5 ( download)
Download or read book Almost Automorphic and Almost Periodic Functions in Abstract Spaces written by Gaston M. N'Guérékata and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost Automorphic and Almost Periodic Functions in Abstract Spaces introduces and develops the theory of almost automorphic vector-valued functions in Bochner's sense and the study of almost periodic functions in a locally convex space in a homogenous and unified manner. It also applies the results obtained to study almost automorphic solutions of abstract differential equations, expanding the core topics with a plethora of groundbreaking new results and applications. For the sake of clarity, and to spare the reader unnecessary technical hurdles, the concepts are studied using classical methods of functional analysis.
Author : Samuel Zaidman
Publisher : Pitman Advanced Publishing Program
ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.55/5 ( download)
Download or read book Almost-periodic Functions in Abstract Spaces written by Samuel Zaidman and published by Pitman Advanced Publishing Program. This book was released on 1985 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research not presents recent results in the field of almost-periodicity. The emphasis is on the study of vector-valued almost-periodic functions and related classes, such as asymptotically almost-periodic or almost-automorphic functions. Many examples are given, and applications are indicated. The first three chapters form a self-contained introduction to the study of continuity, derivability and integration in locally convex or Banach spaces. The remainder of the book is devoted to almost-periodicity and related topics. The functions are defined on IR, IR[superscript n] or an abstract group; the range is a Banach or a Hilbert space. Although treatment of the material related to pure mathematics, the theory has many applications in the area of abstract differential equations.
