5 edition of **Almost periodic type functions and ergodicity** found in the catalog.

- 311 Want to read
- 9 Currently reading

Published
**2003**
by Science Press, Kluwer Academic Publishers in Beijing, New York, Dordrecht, Boston
.

Written in English

- Almost periodic functions,
- Ergodic theory

**Edition Notes**

Includes bibliographical references (p. [335]-350) and index.

Statement | Zhang Chuanyi. |

Classifications | |
---|---|

LC Classifications | QA404 .Z46 2003 |

The Physical Object | |

Pagination | xi, 355 p. ; |

Number of Pages | 355 |

ID Numbers | |

Open Library | OL3706704M |

ISBN 10 | 7030104897, 140201158X |

LC Control Number | 2003277207 |

OCLC/WorldCa | 51526973 |

Differential equations with piecewise constant argument, which were firstly considered by Cooke and Wiener [], and Shah and Wiener [], usually describe hybrid dynamical systems (a combination of continuous and discrete) and so combine properties of both differential and difference the years, great attention has been paid to the study of the Author: Li Wang, Chuanyi Zhang. This treatment of analysis on semigroups stresses the functional analytical and dynamical theory of continuous representations of semitopological semigroups. Topics covered include compact semitopological semigroups, invariant means and idempotent means on compact semitopological semigroups, affine compactifications, left multiplicatively continuous functions and weakly left Reviews: 1.

In probability theory, an ergodic system is a stochastic process which proceeds in time and which has the same statistical behavior averaged over time as over the system's entire possible state modern, formal statement of ergodicity relies heavily on measure theory.. The idea of ergodicity was born in the field of thermodynamics, where it was necessary to relate the . Recently, in [1, 2], Diagana introduced the concept of Stepanov-like pseudo-almost periodicity, which is a generalization of the classical notion of pseudo-almost periodicity, and established some properties for Stepanov-like pseudo-almost periodic er, Diagana studied the existence of pseudo-almost periodic solutions to the abstract semilinear Cited by:

Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and uniqueness of almost automorphic solutions are by: 5. A generalization of almost-periodic functions defined on $ \mathbf R $. Let $ G $ be an (abstract) group. A bounded complex-valued function $ f(x) $, $ x \in G $, is called a right almost-periodic function if the family $ f (x a) $, where $ a $ runs through the entire group $ G $, is (relatively) compact in the topology of uniform convergence on $ G $, i.e. if every sequence of functions $ .

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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 Cited by: 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. Almost periodic type functions -- Almost periodic functions -- Asymptotically almost periodic functions -- Weakly almost periodic functions -- Approximate theorem and applications -- Almost periodic type functions and ergodicity book almost periodic functions -- Converse problems of Fourier expansions -- Almost periodic type sequences -- Ch.

Almost. The Paperback of the Almost Periodic Type Functions and Ergodicity by Zhang Chuanyi at Barnes & Noble.

FREE Shipping on $35 or more. Due to COVID, orders may be delayed. Thank you for your patience. Book Annex Membership Educators Gift Cards Stores & Events Help Auto Suggestions are available once you type at least 3 letters.

Almost Periodic Type Functions and Ergodicity (In English) [Unknown] on *FREE* shipping on qualifying offers. Almost Periodic Type Functions and Ergodicity (In English)Author: Unknown. Motivation.

There are several inequivalent definitions of almost periodic functions. The first was given by Harald interest was initially in finite Dirichlet fact by truncating the series for the Riemann zeta function ζ(s) to make it finite, one gets finite sums of terms of the type (+) with s written as (σ + it) – the sum of its real part σ and imaginary part it.

The theory of almost periodic functions was first developed by the Danish mathematician H. Bohr during Then Bohr's work was substantially extended by S. Bochner, H. Weyl, A.

Besicovitch, J. Favard, J. von Neumann, V. Stepanov, N. Bogolyubov, and oth ers. Generalization of the classical theory of almost periodic functions has been taken in several. 《Almost Periodic Type Functions and Ergodicity》为我们提供了大量的应用微分方程，泛函方程和演化方程的概周期型功能全面的理论。此外，它也提出了关于遍历性和功能谱，界线性算子半群和动力系统理论及其应用的基本理论。它反映了近年来在该领域建立新的。Author: Chuanyi Zhang.

Almost Periodic Type Functions and Ergocity. Book Mild solutions.- Weakly almost periodic solutions.- 4 Ergodicity and averaging methods.- Ergodicity and its properties.- Author: Chuanyi Zhang. Read Free Almost Periodic Type Functions And Ergodicity Almost Periodic Type Functions And Ergodicity Right here, we have countless book almost periodic type functions and ergodicity and collections to check out.

We additionally manage to pay for variant types and as well as type of the books to browse. The usual book, fiction, history, novel.

This book provides a comprehensive theory of almost Periodic type functions with a large number of the applications to differential equations, functional equations and evolution equations.

In addition, it also presents a basic theory on ergodicity and its applications in the theory of function spectrum, semi group of bounded linear operators and dynamical systems. Almost Periodic Function a function whose value is approximately repeated when its argument is increased by properly selected constants (the almost periods).

More precisely, a continuous function f(x) defined for all real values of 5 x is called almost periodic if for every ∊ > 0 there exists an l = l (∊) such that in every interval of length l on.

Permanence and Almost Periodic Solutions of a Discrete Ratio-Dependent Leslie System with Time Delays and Feedback Controls Yu, Gang and Lu, Hongying, Abstract and Applied Analysis, ; The constructive mathematics of A. Markov: some reflections Kushner, B.

A., Modern Logic, ; Robust Almost Periodic Dynamics for Interval Neural Networks with Mixed Time Cited by: 4. 1 Almost periodic type functions.- Numerical almost periodic functions.- Uniform almost periodic functions.- Vector-valued almost periodic functions.- Asymptotically Author: Toka Diagana.

When time scale or, our definition of the uniformly almost periodic functions is equivalent to the classical definitions of uniformly almost periodic functions and the uniformly almost periodic sequences, respectively.

Then, based on these, we study the existence and uniqueness of almost periodic solutions and derive some fundamental Cited by: A consequence of the definition of the classes of almost-periodic functions through the concept of closure is the approximation theorem: For every almost-periodic function $ f (x) $ from $ U $(or $ S ^ {p} $ or $ W ^ {p} $) and every $ \epsilon > 0 $ there is a finite trigonometric polynomial $ P (x) $ in $ T $, satisfying the inequality.

Yoshizawa, Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Applied Mathematical Scien Springer-Verlag, C. Zhang, Almost Periodic Type Functions and Ergodicity, Science Press/Kluwer Academic Publishers, Almost Periodic Type Functions and Ergodicity The theory of almost periodic functions was first developed by the Danish mathematician H.

Bohr during Then Bohr's work was substantially extended by S. Bochner, H. Weyl, A. Besicovitch, J. Favard, J. von Neumann, V. Stepanov, N. This book provides a comprehensive theory of almost periodic type functions with a large number of the applications to differential equations，functional equations and evolution equations.

In addition，it also presents a basic theory on ergodicity and its applications in the theory of function spectrum，semi group of bounded linear operators. We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈ is a family of infinitesimal generators such that for all t ∈, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed.

The following are some important properties of almost periodic functions: (1) An almost periodic function is bounded and uniformly continuous on the entire x-axis. (2) The sum and product of a finite number of almost periodic functions is an almost periodic function.

(3) The limit of a uniformly convergent sequence of almost periodic functions.ABSTRACT ERGODIC THEOREMS AND WEAK ALMOST PERIODIC FUNCTIONS «BY W. F. EBERLEIN Although the individual ergodic theorem of G. D. Birkhoff is sharper than the mean ergodic theorem of J.

von Neumann, it was soon evident that the measure-theoretic formulation obscured the greater generality of the latter result."Once Bohr established his fundamental theorem, he was able to show that any continuous almost periodic function is the limit of a uniformly convergent sequence of trigonometric polynomials.

This is the main result of his second paper. the converse of this result was also true.".