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Topics in Almost Automorphy - Gaston M. N'Guerekata

Topics in Almost Automorphy

Hardcover Published: 15th December 2004
ISBN: 9780387228464
Number Of Pages: 168

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This monograph presents recent contributions to the topics of almost periodicity and almost automorphy. Several new methods, including the methods of invariant subspaces and uniform spectrum, as well as various classical methods, such as fixed point theorems, are used to obtain almost periodic and almost automorphic solutions to some linear and non-linear evolution equations and dynamical systems. Almost periodicity and almost automorphy are also intensively developed on the more general structures called fuzzy-number type spaces. They have further potential applications to the study of differential equations, which model the real-world problems governed by imprecision due to uncertainty or vagueness, rather than randomness. In conclusion, the author indicates several open problems and directions for future research. This monograph is a great source of information and inspiration for researchers and graduate students from many mathematical fields.

Introduction and Preliminaries
Measurable Functions
Sobolev Spaces
Semigroups of Linear Operators
Fractional Powers of Operators
Evolution Equations
Almost Automorphic Functions
Asymptotically Almost Automorphic Functions
Applications to Abstract Dynamical Systems
Almost Periodic Functions
Bibliographical Remarks and Open Problems
Almost Automorphic Evolution Equations
Linear Equations
The inhomogeneous equation x' = Ax + f
Method of Invariant Subspaces
Almost Automorphic Solutions to Some Second-Order Hyperbolic Equations
Nonlinear Equations
Existence of Almost Automorphic Mild Solutions-Case I
Existence of Almost Automorphic Mild Solutions-Case II
Optimal weak-almost periodic solutions
Existence of Weakly Almost Automorphic Solutions
A Correspondence Between Linear and Nonlinear Equations
Almost Periodicity in Fuzzy Setting
Fuzzy Sets
Almost Periodicity in Fuzzy Setting
Harmonics of Almost Periodic Functions in Fuzzy Setting
Applications to Fuzzy Differential Equations
Bibliographical Remarks and Open Problems
Almost Automorphy in Fuzzy Setting
Introduction
Preliminaries
Basic Definitions and Properties
Applications to Fuzzy Differential Equations
Bibliographical Remarks and Open Problems
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387228464
ISBN-10: 0387228462
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 168
Published: 15th December 2004
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 25.4 x 17.78  x 1.27
Weight (kg): 0.54

Earn 363 Qantas Points
on this Book