Displaying similar documents to “A note on wavelet bases in function spaces”

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.

Quantitative properties of quadratic spline wavelet bases in higher dimensions

Černá, Dana, Finěk, Václav, Šimůnková, Martina

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To use wavelets efficiently to solve numerically partial differential equations in higher dimensions, it is necessary to have at one’s disposal suitable wavelet bases. Ideal wavelets should have short supports and vanishing moments, be smooth and known in closed form, and a corresponding wavelet basis should be well-conditioned. In our contribution, we compare condition numbers of different quadratic spline wavelet bases in dimensions d = 1, 2 and 3 on tensor product domains (0,1)^d. ...

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.

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].

Differential and integral calculus for a Schauder basis on a fractal set (I) (Schauder basis 80 years after)

Julian Ławrynowicz, Tatsuro Ogata, Osamu Suzuki (2009)

Banach Center Publications

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In this paper we introduce a concept of Schauder basis on a self-similar fractal set and develop differential and integral calculus for them. We give the following results: (1) We introduce a Schauder/Haar basis on a self-similar fractal set (Theorems I and I'). (2) We obtain a wavelet expansion for the L²-space with respect to the Hausdorff measure on a self-similar fractal set (Theorems II and II'). (3) We introduce a product structure and derivation on a self-similar fractal set (Theorem...