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.

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.

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.

Download or read book Almost Automorphic and Almost Periodic Functions in Abstract Spaces written by Gaston M. N'Guerekata and published by . This book was released on 2014-01-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Almost Periodic Functions in Abstract Spaces written by Samuel Zaidman and published by Longman Sc & Tech. This book was released on 1985-07-01 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

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.

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 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Almost Periodic Solutions of Differential Equations in Banach Spaces written by Yoshiyuki Hino and published by CRC Press. This book was released on 2001-10-25 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 an original decomposition technique. The book also extends classical techniques, such as fixed points and stability methods, to abstract functional differential equations with applications to partial functional differential equations. Almost Periodic Solutions of Differential Equations in Banach Spaces will appeal to anyone working in mathematical analysis.

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.

Download or read book Topics in Almost Automorphy written by Gaston M. N'Guérékata and published by Springer Science & Business Media. This book was released on 2007-07-10 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of our first book [80], there has been a real resiu-gence of interest in the study of almost automorphic functions and their applications ([16, 17, 28, 29, 30, 31, 32, 40, 41, 42, 46, 51, 58, 74, 75, 77, 78, 79]). New methods (method of invariant s- spaces, uniform spectrum), and new concepts (almost periodicity and almost automorphy in fuzzy settings) have been introduced in the literature. The range of applications include at present linear and nonlinear evolution equations, integro-differential and functional-differential equations, dynamical systems, etc...It has become imperative to take a bearing of the main steps of the the ory. That is the main purpose of this monograph. It is intended to inform the reader and pave the road to more research in the field. It is not a self contained book. In fact, [80] remains the basic reference and fimdamental source of information on these topics. Chapter 1 is an introductory one. However, it contains also some recent contributions to the theory of almost automorphic functions in abstract spaces. VIII Preface Chapter 2 is devoted to the existence of almost automorphic solutions to some Unear and nonUnear evolution equations. It con tains many new results. Chapter 3 introduces to almost periodicity in fuzzy settings with applications to differential equations in fuzzy settings. It is based on a work by B. Bede and S. G. Gal [40].

Download or read book Almost Periodic Stochastic Processes written by Paul H. Bezandry and published by Springer Science & Business Media. This book was released on 2011-04-07 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

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 734 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.

Download or read book Studies in Evolution Equations and Related Topics written by Gaston M. N'Guérékata and published by Springer Nature. This book was released on 2021-10-27 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features recent development and techniques in evolution equations by renown experts in the field. Each contribution emphasizes the relevance and depth of this important area of mathematics and its expanding reach into the physical, biological, social, and computational sciences as well as into engineering and technology. The reader will find an accessible summary of a wide range of active research topics, along with exciting new results. Topics include: Impulsive implicit Caputo fractional q-difference equations in finite and infinite dimensional Banach spaces; optimal control of averaged state of a population dynamic model; structural stability of nonlinear elliptic p(u)-Laplacian problem with Robin-type boundary condition; exponential dichotomy and partial neutral functional differential equations, stable and center-stable manifolds of admissible class; global attractor in Alpha-norm for some partial functional differential equations of neutral and retarded type; and more. Researchers in mathematical sciences, biosciences, computational sciences and related fields, will benefit from the rich and useful resources provided. Upper undergraduate and graduate students may be inspired to contribute to this active and stimulating field.