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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Almost Periodic Type Functions and Ergodicity (Paperback, Softcover reprint of the original 1st ed. 2003)
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Almost Periodic Type Functions and Ergodicity (Paperback, Softcover reprint of the original 1st ed. 2003)
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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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