Almost Periodic Type Functions and Ergodicity - Hardcover

Zhang Chuanyi

 
9781402011580: Almost Periodic Type Functions and Ergodicity
Hardcover
ISBN 10: 140201158X ISBN 13: 9781402011580
Verlag: Springer, 2003

Inhaltsangabe

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.

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Críticas

From the reviews:

"In this monograph, the function classes considered are; Bohr almost periodic ... asymptotic ap AAP, Eberlein weakly ap WAP ... and X a Banach space. These are introduced and discussed in some detail; then the author addresses their application to the asymptotic study of solutions of differential equations ... . One should be grateful for the wealth of material presented, collecting, unifying and sometimes generalizing many recent results. Consequently, the book can serve as an introduction ... and it would be especially good for seminars." (Hans F. Günzler, Zentralblatt MATH, Vol. 1068 (19), 2005)

Reseña del editor

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.

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Verlag
Springer
Erscheinungsdatum
2003
Sprache
Englisch
ISBN 10 
140201158X
ISBN 13 
9781402011580
Einband
Tapa dura
Anzahl der Seiten
372
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
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Hamburg
Deutschland

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