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. WebBanach space. Definition. A B.U.L. function X(t) is called generalized almost periodic if and only if for each given e > 0 there exists a number L > 0 such that in every interval of the real line of length L there is at least one number r satisfying The family of all generalized almost periodic functions will be designated
Hierarchy of almost-periodic function spaces
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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 …
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 ... 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.
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. Web24 de mai. de 2024 · Abstract. In this paper we investigate the asymptotic behaviour of the classical continuous and unbounded almost periodic function in the Lebesgue …
Webproviding 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.
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 … city clerk belleville ilWebThe 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 … dictatorship summaryWebThe definition of an almost periodic function given by Bohr in his pioneering work [Reference Bohr 6] is based on two properly generalized concepts: the periodicity to the so-called almost periodicity, and the periodic distribution of periods to the so-called relative density of almost periods. city clerk association wisconsinWeb17 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 … city clerk billings mtWebBook Title Almost-Periodic Functions and Functional Equations. Authors Luigi Amerio, Giovanni Prouse. Series Title The university series in higher mathematics. DOI … dictatorships ww2WebWe 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. city clerk buffalo new yorkWebThe various types of definitions of almost-periodic functions are examined and compared in order to clarify the hierarchy of almost-periodic function spaces. … city clerk binghamton ny