3 edition of **Almost-periodic functions and functional equations** found in the catalog.

Almost-periodic functions and functional equations

Luigi Amerio

- 67 Want to read
- 5 Currently reading

Published
**1970** by Van Nostrand Reinhold in New York .

Written in English

- Almost periodic functions,
- Functional equations,
- Banach spaces

**Edition Notes**

Bibliography: p. 179-183.

Statement | [by] Luigi Amerio and Giovanni Prouse. |

Series | The University series in higher mathematics |

Contributions | Prouse, Giovanni, joint author. |

Classifications | |
---|---|

LC Classifications | QA404 .A46 |

The Physical Object | |

Pagination | viii, 184 p. |

Number of Pages | 184 |

ID Numbers | |

Open Library | OL5314462M |

LC Control Number | 72112713 |

AbstractIn this paper, the exponential dichotomy, and Tikhonov and Banach fixed point theorems are used to study the existence and uniqueness of pseudo almost periodic solutions of a class of iterative functional differential equations of the form x′(t)=∑n=1k∑l=1∞Cl,n(t)(x[n](t))l+G(t), $$\begin{array}{} \displaystyle x'(t)=\sum_{n=1}^k\sum_{l=1}^\infty C_{l, n}(t)(x^{[n]}(t))^l+G(t Cited by: 1. 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. The notion of stability of functional equations has its origins with S. M. Ulam, who posed the fundamental problem for approximate homomorphisms in and with D. H. Hyers, Th. M. Rassias, who provided the first significant solutions for additive and linear mappings in and , : Springer New York.

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Almost-Periodic Functions and Functional Equations. Authors (view affiliations) Luigi Amerio; Almost-Periodic Functions in Banach Spaces. Luigi Amerio, Giovanni Prouse Pages Applications Almost-periodic functions and functional equations book Almost-Periodic Functional Equations.

Front Matter. Pages PDF. The Wave Equation. Luigi Amerio, Giovanni Prouse. Pages The. Almost-Periodic Functions and Functional Equations It seems that you're in USA. We have a dedicated site for USA Almost-Periodic Functions and Functional Equations.

Authors: Amerio, L., Prouse, G Free Preview. Buy this book eB84 € price for Spain (gross) Buy eBook ISBN. Almost-periodic functions and functional equations by Amerio, Luigi Prouse, Giovanni, and a great selection of related books, art and collectibles available now at 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.

Get this from a library. Almost-periodic functions and functional equations. [Luigi Amerio]. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

The theory of almost-periodic functions with complex values, created by H. Bohr [1] in his two classical papers published in Acta Mathematica in andhas been developed by many authors and has had note worthy applications: we recall the works of Weyl, De la Vallee Poussin, Bochner, Stepanov, Wiener, Besicovic, Favard, Delsarte, Maak, Bogoliu bov, : Paperback.

Completely new is [Chapter II.3], which is devoted to a relatively new class of almost periodic functions: random functions almost periodic in probability. It is certain that these functions will find many applications in the theory of stochastic functional equations.''Format: Hardcover.

Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more. Linear constant coefficient equations.- Linear almost periodic equations.- Exponential dichotomy and kinematic similarity.- Fixed point methods.- Asymptotic almost periodic functions and other Author: Toka Diagana.

Asymptotically almost periodic solutions to some classes of second-order functional differential equations Diagana, Toka, Henriquez, Hernán, and Hernández, Eduardo, Differential and Integral Equations, ; Almost Periodic Sequence Solutions of a Discrete Predator-Prey System with Beddington-DeAngelis Functional Response Du, Zengji and Li Cited by: 4.

Completely new is [Chapter II.3], which is devoted to a relatively new class of almost periodic functions: random functions almost periodic in probability.

It is certain that these functions will find many applications in the theory of stochastic functional equations.”.

Almost periodic functions occur frequently as a result of sampling a continuous-time periodic function and the functional dependence on two or more purely periodic functions with incommensurate Author: Constantin Corduneanu.

The paper is aimed at providing some results on the almost periodicity of solutions to some general functional or functional differential equations. The term “general” is meant in the sense that the equations involve operators of general form, acting on the space of almost periodic functions. First order and second order equations are dealt Cited by: 2.

The purpose of this book is to provide an overall view of all the basic features of almost periodic functions, in the various meanings this term has acquired in modern research, as well as the many applications of such functions. In this paper we study a non-autonomous neutral functional differential equation in a Banach space.

Applying the theory of semigroups of operators to evolution equations and Krasnoselskii’s fixed point theorem we establish the existence and uniqueness of a mild almost periodic solution of the problem under by: We first propose a concept of almost periodic functions in the sense of Stepanov on time scales.

Then, we consider a class of neutral functional dynamic equations with Stepanov-almost periodic terms on time scales in a Banach space.

By means of the contraction mapping principle, we establish some criteria for the existence and uniqueness of almost periodic solutions for this class of dynamic Cited by: 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.

Princeton University Library One Washington Road Princeton, NJ USA () 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 theory of almost periodic functions was created and developed in its main features by Bohr as a generalization of pure periodicity. Almost periodicity is a structural property of functions, which is invariant with respect to the operations of addition and multiplication, and also in some cases with respect to division, differentiation, integration, and other limiting processes.

where and, are closed linear operators; is a Banach space; the history, belongs to some abstract phase space defined axiomatically are appropriated functions. The study of abstract neutral equations is motivated by different practical applications in different technical fields. The literature related to ordinary neutral functional differential equations is very extensive and we refer Cited by: The book also extends classical techniques, such as fixed points and stability methods, to abstract functional differential equations with applications to partial functional differential equations.

Almost Periodic Solutions of Differential Equations in Banach Spaces will appeal to anyone working in mathematical analysis. Almost Automorphic and Almost Periodic Functions in Abstract Spaces introduces and develops the theory of almost automorphic vector-valued functions in Bochner's sense and the study of almost periodic functions in a locally convex space in a homogenous and unified manner.

It also applies the results obtained to study almost automorphic solutions of abstract differential equations, expanding. Table of contents for Pseudo almost periodic functions in Banach spaces / Toka Diagana.

Bibliographic record and links to related information available from the Library of Congress catalog. Note: Contents data are machine generated based on pre-publication provided by the publisher. In this paper, by employing matched spaces for time scales, we introduce a δ -almost periodic function and obtain some related properties.

Also the hull equation for homogeneous dynamic equation is introduced and results of the existence are presented. In the sense of admitting exponential dichotomy for the homogeneous equation, the expression of a δ -almost periodic solution for a type Author: Chao Wang, Ravi P.

Agarwal, Donal O’Regan. The purpose of this paper is to extend in Section 3 the main properties of almost periodic functions with values in Banach spaces, to the class of almost periodic functions with values in other important abstract spaces in Functional Analysis, namely the p-Frechet spaces, 0.

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 directions.

One direction is. Almost Periodic Case Trigonometric Polynomials and AP r-Spaces, Some Properties of the Spaces AP r(R,C), AP r-Solutions to Ordinary Differential Equations, AP r-Solutions to Convolution Equations, Oscillatory Solutions Involving the Space B, Oscillatory Motions Described by Classical Almost.

The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields Author: Constantin Corduneanu.

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 Author: Zhang Chuanyi. Buy Almost-Periodic Functions and Functional Equations by L. Amerio, G. Prouse from Waterstones today. Click and Collect from your local Waterstones Pages: (ii) there is a trigonometric polynomial where such that (iii)for all real sequence there is a subsequence such that converges uniformly on.

Definition One saysthat a continuous function is almost periodicif and only if satisfies one of the three conditions of Proposition A number verifying () is called almost period. By using Proposition we get the following property of Cited by: 4. Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics.

The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and. Read "Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces" by Toka Diagana available from Rakuten Kobo.

This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, al Brand: Springer International Publishing. of almost periodic solutions of functional-differential equations.

In this chapter; therefore, we give a "brief discussion of the development of almost periodicity and functional-differential equations. Almost periodicity as a structural property of functions is a generalization of.

In this paper we study the existence of almost periodic solutions for linear retarded functional differential equations with finite delay and values in a Banach space. We relate the existence of almost periodic solutions with the stabilization of distributed control systems.

We apply our results to transport models and to the wave by: 2. Author of Funcții aproape-periodice, Principles of differential and integral equations, Principles of differential and integral equations, Almost periodic functions, Almost Periodic Oscillations and waves, Functional equations with causal operators, Integral equations and applications, Integral equations and stability of feedback systemsWritten works: Integral Equations And Applications, Almost Periodic Functions.

Luigi Amerio (15 August – 28 September ), was an Italian electrical engineer and is known for his work on almost periodic functions, on Laplace transforms in one and several dimensions, and on the theory of elliptic partial differential equationsAlma mater: Polytechnic University of Milan.

Weyl-almost periodic solutions and asymptotically Weyl-almost periodic solutions of abstract Volterra integro-differential equations Kostić, Marko, Banach Journal of Mathematical Analysis, Almost automorphic solutions of semilinear stochastic hyperbolic differential equations in intermediate space Xia, Zhinan, Kodai Mathematical Journal, Cited by: 2.

I am currently studying Ergodic Theory from Glasner’s book - in it, weakly almost periodic functions play a large role, as well as general “means” and unitary representations of groups on Hilbert spaces. I cannot seem to grasp the motivation or intuition behind these notions."This monograph deals with several aspects of the functional differential equations theory, viz., the problem of existence (local and global) and uniqueness of solutions, stability, and oscillatory motions (periodic and almost periodic) This book will be useful to people working on functional differential equations and their applications to science, engineering and economics.".[1] L.

Amerio and G. Prouse, Almost-periodic Functions and Functional Equations, Van Nostrand Reinhold Co.,New York-Toronto, Ont.-Melbourne, viii+ pp. Google Scholar [2] L. Arnold and C. Tudor, Stationary and almost periodic solutions of almost periodic affine stochastic differential equations, Stochastics Stochastics Rep., 64 (), Cited by: 1.