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A generalized strange term in Signorini’s type problems

Carlos Conca, François Murat, Claudia Timofte (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

A Generalized Strange Term in Signorini's Type Problems

Carlos Conca, François Murat, Claudia Timofte (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

Closure of dilates of shift-invariant subspaces

Moisés Soto-Bajo (2013)

Open Mathematics

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...

Completeness in L1(R) of discrete translates.

Joaquim Bruna, Alexander Olevskii, Alexander Ulanovskii (2006)

Revista Matemática Iberoamericana

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.

Fourier approach to homogenization problems

Carlos Conca, M. Vanninathan (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Fourier approach to homogenization problems

Carlos Conca, M. Vanninathan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Generalized Schauder frames

S.K. Kaushik, Shalu Sharma (2014)

Archivum Mathematicum

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...

In a shadow of the RH: Cyclic vectors of Hardy spaces on the Hilbert multidisc

Nikolai Nikolski (2012)

Annales de l’institut Fourier

Completeness of a dilation system ( ϕ ( n x ) ) n ≥ 1 on the standard Lebesgue space L 2 ( 0 , 1 ) is considered for 2-periodic functions ϕ . We show that the problem is equivalent to an open question on cyclic vectors of the Hardy space H 2 ( 𝔻 2 ∞ ) on the Hilbert multidisc 𝔻 2 ∞ . 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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