Almost periodic and almost automorphic functions in abstract spaces / Gaston M. N'Guérékata.
2021
QA351
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Title
Almost periodic and almost automorphic functions in abstract spaces / Gaston M. N'Guérékata.
Edition
2nd ed.
ISBN
9783030737184 (ebook)
3030737187 (ebook)
3030737179 (print)
9783030737177 (print)
3030737187 (ebook)
3030737179 (print)
9783030737177 (print)
Publication Details
Cham : Springer, 2021.
Language
English
Description
1 online resource (137 pages)
Item Number
10.1007/978-3-030-73718-4 doi
Call Number
QA351
Dewey Decimal Classification
515/.9
Summary
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
Bibliography, etc. Note
Includes bibliographical references.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed June 14, 2021).
Available in Other Form
Almost Periodic and Almost Automorphic Functions in Abstract Spaces
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Table of Contents
1. Introduction and Preliminaries
2. Almost Automorphic Functions
3. Almost Automorphy of the Function f(t, x)
4. Differentiation and Integration
5. Pseudo Almost Automorphy
6. Stepanov-like Almost Automorphic Functions
7. Dynamical Systems and C0-Semigroups
8. Almost Periodic Functions with Values in a Locally Convex Space
9. Almost Period Functions with Values in a Non-Locally Convex Space
10. The Equation x'(t)=A(t)x(t)+f(t)
11. Almost Periodic Solutions of the Differential Equation in Locally Convex Spaces
Bibliography.
2. Almost Automorphic Functions
3. Almost Automorphy of the Function f(t, x)
4. Differentiation and Integration
5. Pseudo Almost Automorphy
6. Stepanov-like Almost Automorphic Functions
7. Dynamical Systems and C0-Semigroups
8. Almost Periodic Functions with Values in a Locally Convex Space
9. Almost Period Functions with Values in a Non-Locally Convex Space
10. The Equation x'(t)=A(t)x(t)+f(t)
11. Almost Periodic Solutions of the Differential Equation in Locally Convex Spaces
Bibliography.