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Author: Toka Diagana Publisher: Springer Science & Business Media ISBN: 3319008498 Category : Mathematics Languages : en Pages : 303
Book Description
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: Toka Diagana Publisher: Springer Science & Business Media ISBN: 3319008498 Category : Mathematics Languages : en Pages : 303
Book Description
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: Gaston M. N'Guérékata Publisher: Springer Science & Business Media ISBN: 147574482X Category : Mathematics Languages : en Pages : 143
Book Description
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: Gaston M. N'Guérékata Publisher: Springer Nature ISBN: 3030737187 Category : Mathematics Languages : en Pages : 134
Book Description
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: Marko Kostić Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110763605 Category : Mathematics Languages : en Pages : 606
Book Description
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: Samuel Zaidman Publisher: Boston : Pitman Advanced Pub. Program ISBN: Category : Almost-periodic functions Languages : en Pages : 148
Book Description
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.
Author: Marko Kostić Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110641852 Category : Mathematics Languages : en Pages : 372
Book Description
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: 3110763524 Category : Mathematics Languages : en Pages : 734
Book Description
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: Marko Kostic Publisher: CRC Press ISBN: 148225431X Category : Mathematics Languages : en Pages : 484
Book Description
The theory of linear Volterra integro-differential equations has been developing rapidly in the last three decades. This book provides an easy to read concise introduction to the theory of ill-posed abstract Volterra integro-differential equations. A major part of the research is devoted to the study of various types of abstract (multi-term) fractional differential equations with Caputo fractional derivatives, primarily from their invaluable importance in modeling of various phenomena appearing in physics, chemistry, engineering, biology and many other sciences. The book also contributes to the theories of abstract first and second order differential equations, as well as to the theories of higher order abstract differential equations and incomplete abstract Cauchy problems, which can be viewed as parts of the theory of abstract Volterra integro-differential equations only in its broad sense. The operators examined in our analyses need not be densely defined and may have empty resolvent set. Divided into three chapters, the book is a logical continuation of some previously published monographs in the field of ill-posed abstract Cauchy problems. It is not written as a traditional text, but rather as a guidebook suitable as an introduction for advanced graduate students in mathematics or engineering science, researchers in abstract partial differential equations and experts from other areas. Most of the subject matter is intended to be accessible to readers whose backgrounds include functions of one complex variable, integration theory and the basic theory of locally convex spaces. An important feature of this book as compared to other monographs and papers on abstract Volterra integro-differential equations is, undoubtedly, the consideration of solutions, and their hypercyclic properties, in locally convex spaces. Each chapter is further divided in sections and subsections and, with the exception of the introductory one, contains a plenty of examples and open problems. The numbering of theorems, propositions, lemmas, corollaries, and definitions are by chapter and section. The bibliography is provided alphabetically by author name and a reference to an item is of the form, The book does not claim to be exhaustive. Degenerate Volterra equations, the solvability and asymptotic behaviour of Volterra equations on the line, almost periodic and positive solutions of Volterra equations, semilinear and quasilinear problems, as some of many topics are not covered in the book. The author’s justification for this is that it is not feasible to encompass all aspects of the theory of abstract Volterra equations in a single monograph.
Author: Toka Diagana
Author: Toka Diagana
Author: Gaston M. N'Guérékata
Author: Gaston M. N'Guérékata
Author: Gaston M. N'Guerekata
Author: Marko Kostić
Author: Samuel Zaidman
Author: Marko Kostić
Author: Marko Kostić
Author: Marko Kostić
Author: Marko Kostic