Hierarchy of almost-periodic function spaces
WebThe various types of definitions of almost-periodic functions are examined and compared in order to clarify the hierarchy of almost-periodic function spaces. Apart from the standard … 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 …
Hierarchy of almost-periodic function spaces
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WebIn 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 … WebAbout this book. Almost Automorphic and Almost Periodic Functions in Abstract Spaces introduces and develops the theory of almost automorphic vector-valued functions in …
Web1 de jan. de 2011 · Abstract This paper contains a construction of a scale of almost periodic functions spaces, extending from the space of functions representable as … Webrecurrent functions, and Doss almost periodic functions in Lebesgue spaces with variable exponents were analyzed in the first part of this research study by Kostic´ and Du [13]. As mentioned in the abstract, the main aim of this paper was to analyze several different notions of almost periodic type functions and uniformly recurrent type ...
Web24 de mar. de 2024 · Almost Periodic Function. A function representable as a generalized Fourier series. Let be a metric space with metric . Following Bohr (1947), a … 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 ...
Web14 de abr. de 2024 · The main aim of this survey article is to present several known results about vector-valued almost periodic functions and their applications. We separately consider almost periodic functions depending on one real variable and almost periodic functions depending on two or more real variables. We address several open problems …
WebBook Title Almost-Periodic Functions and Functional Equations. Authors Luigi Amerio, Giovanni Prouse. Series Title The university series in higher mathematics. DOI … greenfinch grove birchwood warringtonWebA 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. greenfinch homes limitedWebWe can see that M2 is an example of a nonseparable Hilbert space because the collection eiξx is orthonormal for all ξ ∈ R. We can look at the subspace Bp ⊆ Mp of elements spanned by these functions, called the Besicovitch almost periodic functions. We can see that B2 ≠ M2 since there are functions like. f(x) = { 1 x ≥ 0 − 1 x < 0. greenfinch femaleWeb1 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. flush cache bmcWebAlmost periodic functions in a group, I [l].f Its main object is to extend the theory of almost periodicity to those functions having values which are not numbers but elements of a general linear space L. For functions of a real variable this extension was begun by Bochner [2], and then applied ... greenfinch hen for saleWebvector space containing all the continuous periodic functions, one sees that every element of this vector space satisfies Condition A. If one now completes the space by using the topology of uniform convergence on R, then one gets the linear space of all functions satisfying Condition A. We call this space AP, the space of almost periodic ... flush cache commandWeb[5] Hierarchy of almost-periodic function spaces 125 Proposition 2.3.([4, p. 5], [22, p. 2], [76, p. 155]) Every u.a.p. function is uniformly continuous. Proposition 2.4.([4, p. 5], [22, p. … flush cache ax2012