Hierarchy of almost-periodic function spaces

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August undefined, 2024

In mathematics, an almost periodic function is, loosely speaking, a function of a real number that is periodic to within any desired level of accuracy, given suitably long, well-distributed "almost-periods". The concept was first studied by Harald Bohr and later generalized by Vyacheslav Stepanov, Hermann Weyl and Abram Samoilovitch Besicovitch, amongst others. There is also a notion of almost periodic functions on locally compact abelian groups, first studied by John von N… WebAbstract. It is not the purpose of this paper to construct approximations but to establish a class of almost periodic functions which can be approximated, with an arbitrarily prescribed accuracy, by continuous periodic functions uniformly on ℝ= (∞+∞). Download to read the full article text.

Hierarchy of almost-periodic function spaces - Semantic Scholar

Web1 de abr. de 2024 · Almost-periodic function A function representable as a generalized Fourier series. There are several ways of defining classes of almost-periodic … WebDiscusses basic properties of almost automorphic functions in Banach spaces and their generalizations. Presents open problems for almost periodicity in nonlocally convex … shanghai lockdown lift

Hierarchy of almost-periodic function spaces

Web1 de dez. de 2024 · This motivates us to further explore ergodicity of functions in Orlicz spaces. The direct impetus of this work comes from Diagana and Zitane’s paper where a new notion called Stepanov-like pseudo-almost periodic functions in Lebesgue spaces with variable exponents $\mathop {\mathrm{L}}\nolimits ^{p\left( . \right) }$ is explored. WebKey Words: Stepanov p-almost periodic type functions, Weyl p-almost periodic type functions, composition principles, abstract semilinear Cauchy inclusions, Banach spaces. This research was supported by grant 174024 of Ministry of Science and Technological Devel-opment, Republic of Serbia. WebThe definition of an almost periodic function given by Bohr in his pioneering work [ 6] is based on two properly generalized concepts: the periodicity to the so-called almost … shanghai lockdown metal barriers residential

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SOME PROBLEMS IN THE THEORY OF ALMOST PERIODIC FUNCTIONS

Web16 de jun. de 2009 · Furthermore, we cite the articles [14–16] which are devoted to study almost periodic solutions of difference equations, but a little is known about almost periodic solutions, and in particular, for periodic solutions of nonlinear functional difference equations in phase space via uniform stability, uniformly asymptotically … WebBook Title Almost-Periodic Functions and Functional Equations. Authors Luigi Amerio, Giovanni Prouse. Series Title The university series in higher mathematics. DOI … shanghai lockdown latest updateWeb31 de ago. de 2013 · Jun 2013. Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces. pp.1-41. Toka Diagana. In this introductory chapter, we collect the basic background on metric, Banach, and ... shanghai lockdown march 2022

"WebSince the publication of Almost automorphic and almost periodic functions in abstract spaces (Kluwer Academic/Plenum, 2001), there has been a surge of interest in the theory of almost automorphic functions and applications to evolution equations. Several generalizations have since been introduced in the literature, including the study of almost ... " - Hierarchy of almost-periodic function spaces

Hierarchy of almost-periodic function spaces

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Web17 de ago. de 2024 · Vector Spaces: sets with operations of "addition" and "(scalar) multiplication". Topological Vector Spaces: "addition" and "multiplication" are continuous … Web16 de jan. de 2024 · The various types of definitions of almost-periodic functions are examined and compared in order to clarify the hierarchy of almost-periodic function …

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Web15 de set. de 2024 · In this paper, we prove the completeness of the space of weighted Stepanov-like pseudo almost automorphic (periodic) functions under weak conditions. That is, for every ρ ∈ U ∞, the space of weighted Stepanov-like pseudo almost automorphic (periodic) functions is complete under the norm ‖ ⋅ ‖ S p. Web31 de ago. de 2013 · We study the superposition operators (also called Nemytskii operators) between spaces of almost periodic (respectively almost automorphic) functions in the …

Web23 de abr. de 2024 · If we want to indicate the dependence on the underlying measure space, we write Lp(S, S, μ). Of course, L1 is simply the collection of functions that are integrable with respect to μ. Our goal is to study the spaces Lp for p ∈ (0, ∞]. We start with some simple properties. Suppose that f: S → R is measurable. Web1 de jan. de 2013 · The theory of almost periodic functions was introduced in the literature around 1924–1926 with the pioneering work of the Danish mathematician Bohr [].A decade later, various significant contributions were then made to that theory mainly by Bochner [], von Neumann [], and van Kampen [].The notion of almost periodicity, which generalizes …

WebA particular attention is paid to the Nemytskii operator between spaces of Stepanov--Orlicz almost periodic functions. Finally, we establish an existence and uniqueness result of Bohr almost periodic mild solution to a class of semilinear evolution equations with Stepanov--Orlicz almost periodic forcing term. Web18 de jan. de 2024 · In this paper, we consider an equivalence relation on the space $AP (\mathbb {R},X)$ of almost periodic functions with values in a prefixed Banach space …

Web17 de out. de 2024 · In this paper, we analyze some classes of generalized almost periodic functions with values in ordered Banach spaces. The main structural characterizations …

shanghai lockdown liftedWebThe various types of definitions of almost-periodic functions are examined and compared in order to clarify the hierarchy of almost-periodic function spaces. … shanghai lockdown new variantWebThe various types of definitions of almost-periodic functions are examined and compared in order to clarify the hierarchy of almost-periodic function spaces. … shanghai lockdown riotsWebproviding a uni cation concept for all classes of almost periodic functions examined in [10,26{28]. The Stepanov classes of ˆ-almost periodic functions can be viewed as some very special classes of metrical ˆ-almost periodic functions; as indicated in [19], this is no longer true for the Weyl classes of ˆ-almost periodic functions. shanghai lockdown logisticsWebThe convolution of two almost periodic functions x(t) and y (I) is de fined by x*y(t) = y(s)} and is again an almost periodic function. The Banach space A is a Banach algebra under convolution-multiplication. (For the terminology of the theory of Banach algebras see Loomis [14]). This algebra does not shanghai lockdown periodWeb1 de jan. de 2006 · The various types of definitions of almost-periodic functions are exam ined and compared in order to clarify the hierarchy of almost-periodic function spaces. Apart from the standard... shanghai lockdown pets being killedWebIn mathematics, an almost periodic function is, loosely speaking, a function of a real number that is periodic to within any desired level of accuracy, given suitably long, well-distributed "almost-periods". The concept was first studied by Harald Bohr and later generalized by Vyacheslav Stepanov, Hermann Weyl and Abram Samoilovitch … shanghai lock down period