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The limit behavior of the solutions of Signorini’s type-like problems in periodically perforated domains with period is studied. The main feature of this limit behaviour is the existence of a critical size of the perforations that separates different emerging phenomena as . In the critical case, it is shown that Signorini’s problem converges to a problem associated to a new operator which is the sum of a standard homogenized operator and an extra zero order term (“strange term”) coming from the...
The limit behavior of the solutions of Signorini's type-like
problems in periodically perforated domains with period
ε is studied. The main feature of this limit behaviour is
the existence of a critical size of the perforations that
separates different emerging phenomena as ε → 0. In the critical case, it is shown that Signorini's problem
converges to a problem associated to a new operator which
is the sum of a standard homogenized operator and an extra zero
order term (“strange term”) coming from...
The aim of this paper is to obtain sharp estimates from below of the measure of the set of divergence of the m-fold Fourier series with respect to uniformly bounded orthonormal systems for the so-called G-convergence and λ-restricted convergence. We continue the study begun in a previous work.
Let V be any shift-invariant subspace of square summable functions. We prove that if for some A expansive dilation V is A-refinable, then the completeness property is equivalent to several conditions on the local behaviour at the origin of the spectral function of V, among them the origin is a point of A*-approximate continuity of the spectral function if we assume this value to be one. We present our results also in a more general setting of A-reducing spaces. We also prove that the origin is a...
We characterize, in terms of the Beurling-Malliavin density, the discrete spectra Λ ⊂ R for which a generator exists, that is a function φ ∈ L1(R) such that its Λ translates φ(x - λ), λ ∈ Λ, span L1(R). It is shown that these spectra coincide with the uniqueness sets for certain analytic clases. We also present examples of discrete spectra Λ ∈ R which do not admit a single generator while they admit a pair of generators.
This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems of periodic...
This article is divided into two chapters. The
classical problem of homogenization of elliptic operators with
periodically oscillating coefficients is revisited in the
first chapter. Following a Fourier approach, we discuss some
of the basic issues of the subject: main convergence theorem,
Bloch approximation, estimates on second order derivatives,
correctors for the medium, and so on. The second chapter is
devoted to the discussion of some non-classical behaviour of
vibration problems of periodic...
Schauder frames were introduced by Han and Larson [9] and further studied by Casazza, Dilworth, Odell, Schlumprecht and Zsak [2]. In this paper, we have introduced approximative Schauder frames as a generalization of Schauder frames and a characterization for approximative Schauder frames in Banach spaces in terms of sequence of non-zero endomorphism of finite rank has been given. Further, weak* and weak approximative Schauder frames in Banach spaces have been defined. Finally, it has been proved...
Completeness of a dilation system on the standard Lebesgue space is considered for 2-periodic functions . We show that the problem is equivalent to an open question on cyclic vectors of the Hardy space on the Hilbert multidisc . Several simple sufficient conditions are exhibited, which include however practically all previously known results (Wintner; Kozlov; Neuwirth, Ginsberg, and Newman; Hedenmalm, Lindquist, and Seip). For instance, each of the following conditions implies cyclicity...
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