## Details

**Table of Contents**

Preface

Chapter 1. Preliminaries

Chapter 2. Almost Periodic Functions

Chapter 3. Almost Automorphic Functions and Sequences

Chapter 4. Spectrum of Bounded Functions

Chapter 5. Applications to Differential Equations

Appendix

References

Author’s Contact Information

Index

**Reviews**

“This monograph is devoted to the theory of spectra of bounded functions in abstractspaces. Spectral theory is very important as it gives important qualitative properties ofsolutions to evolution equations. It is particularly useful in the study of the asymptoticbehavior of mild solutions of evolution equations. The monograph is divided into fivechapters. Chapter 1 is about some basic defnitions and notations. Chapter 2 is devotedto the theory of almost periodic functions. These functions have important applicationsin celestial mechanics, control theory and other fields. In chapter 3, the author discussesthe concepts of almost automorphic functions and sequences, which are generalizationsof almost periodic functions and sequences. After these chapters, the author moves onto defining the spectrum of bounded functions, in chapter 4. The concepts of Carleman,Beurling, uniform and circular spectra are defined. The last chapter is devoted to thestudy of difference and first- and second-order differential equations.Overall, this monograph is useful for researchers working in the field of spectraltheory of bounded functions and the qualitative theory of differential equations inabstract spaces. The monograph is written for graduate students, and to read it oneneeds to first go through the basics of abstract spaces and functional analysis.” – Dr. Syed Abbas, Professor, Indian Institute of Technology Mandi, India

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This book is designed for beginning researchers and graduate students in harmonic analysis, functional analysis and evolution equations