A remark on the div-curl lemma

Pierre Gilles Lemarié-Rieusset

Displaying similar documents to “A remark on the div-curl lemma”

Vector-valued wavelets and the Hardy space H¹(ℝⁿ,X)

Tuomas Hytönen (2006)

Studia Mathematica

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We prove an analogue of Y. Meyer's wavelet characterization of the Hardy space H¹(ℝⁿ) for the space H¹(ℝⁿ,X) of X-valued functions. Here X is a Banach space with the UMD property. The proof uses results of T. Figiel on generalized Calderón-Zygmund operators on Bochner spaces and some new local estimates.

Non-MSF Wavelets for the Hardy Space H²(ℝ)

Biswaranjan Behera (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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All wavelets constructed so far for the Hardy space H²(ℝ) are MSF wavelets. We construct a family of H²-wavelets which are not MSF. An equivalence relation on H²-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H²-wavelets with Fourier transform not vanishing in any neighbourhood of the origin.

Recent developments in wavelet methods for the solution of PDE's

Silvia Bertoluzza (2005)

Bollettino dell'Unione Matematica Italiana

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After reviewing some of the properties of wavelet bases, and in particular the property of characterisation of function spaces via wavelet coefficients, we describe two new approaches to, respectively, stabilisation of numerically unstable PDE's and to non linear (adaptive) solution of PDE's, which are made possible by these properties.

A note on wavelet bases in function spaces

Hans Triebel (2004)

Banach Center Publications

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Pointwise smoothness, two-microlocalization and wavelet coefficients.

Stéphane Jaffard (1991)

Publicacions Matemàtiques

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In this paper we shall compare three notions of pointwise smoothness: the usual definition, J.M. Bony's two-microlocal spaces C , and the corresponding definition on the wavelet coefficients. The purpose is mainly to show that these two-microlocal spaces provide "good substitutes" for the pointwise Hölder regularity condition; they can be very precisely compared with this condition, they have more functional properties, and can be characterized by conditions on the wavelet...

Wavelet techniques for pointwise regularity

Stéphane Jaffard (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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Let $E$ be a Banach (or quasi-Banach) space which is shift and scaling invariant (typically a homogeneous Besov or Sobolev space). We introduce a general definition of pointwise regularity associated with $E$ , and denoted by $C_{E}^{α} (x_{0})$ . We show how properties of $E$ are transferred into properties of $C_{E}^{α} (x_{0})$ . Applications are given in multifractal analysis.

A Note on Div-Curl Lemma

Gala, Sadek (2007)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 42B30, 46E35, 35B65. We prove two results concerning the div-curl lemma without assuming any sort of exact cancellation, namely the divergence and curl need not be zero, and $d i v (u^{-} v^{\to}) \in H^{1} (R^{d})$ which include as a particular case, the result of [3].

Wavelet bases for the biharmonic problem

Bímová, Daniela, Černá, Dana, Finěk, Václav

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In our contribution, we study different Riesz wavelet bases in Sobolev spaces based on cubic splines satisfying homogeneous Dirichlet boundary conditions of the second order. These bases are consequently applied to the numerical solution of the biharmonic problem and their quantitative properties are compared.

On the exact values of coefficients of coiflets

Dana Černá, Václav Finěk, Karel Najzar (2008)

Open Mathematics

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In 1989, R. Coifman suggested the design of orthonormal wavelet systems with vanishing moments for both scaling and wavelet functions. They were first constructed by I. Daubechies [15, 16], and she named them coiflets. In this paper, we propose a system of necessary conditions which is redundant free and simpler than the known system due to the elimination of some quadratic conditions, thus the construction of coiflets is simplified and enables us to find the exact values of the scaling...

A note on the construction of nonseparable wavelet bases and multiwavelet matrix filters of $L^{2} (ℝ^{n})$ , where $n \geq 2$ .

Karoui, Abderrazek (2003)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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Construction of Non-MSF Non-MRA Wavelets for L²(ℝ) and H²(ℝ) from MSF Wavelets

Aparna Vyas (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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Considering symmetric wavelet sets consisting of four intervals, a class of non-MSF non-MRA wavelets for L²(ℝ) and dilation 2 is obtained. In addition, we obtain a family of non-MSF non-MRA H²-wavelets which includes the one given by Behera [Bull. Polish Acad. Sci. Math. 52 (2004), 169-178].

A proof of completeness of the Green-Lamé type solution in thermoelasticity.

Chandrasekharaiah, D.S. (1993)

International Journal of Mathematics and Mathematical Sciences

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Wavelet transform for functions with values in UMD spaces

Cornelia Kaiser, Lutz Weis (2008)

Studia Mathematica

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We extend the classical theory of the continuous and discrete wavelet transform to functions with values in UMD spaces. As a by-product we obtain equivalent norms on Bochner spaces in terms of g-functions.