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

Julian Ławrynowicz; Tatsuro Ogata; Osamu Suzuki

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Displaying similar documents to “Differential and integral calculus for a Schauder basis on a fractal set (I) (Schauder basis 80 years after)”

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Arambašić Ljiljana, Damir Bakić, Rajna Rajić (2010)

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The paper is a continuation of our study of dimension functions of orthonormal wavelets on the real line with dyadic dilations. The main result of Section 2 is Theorem 2.8 which provides an explicit reconstruction of the underlying generalized multiresolution analysis for any MSF wavelet. In Section 3 we reobtain a result of Bownik, Rzeszotnik and Speegle which states that for each dimension function D there exists an MSF wavelet whose dimension function coincides with D. Our method...

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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.

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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. ...

Wavelet bases for the biharmonic problem

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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.

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)

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Application of the Haar wavelet method for solution the problems of mathematical calculus

Ü. Lepik, H. Hein (2015)

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In recent times the wavelet methods have obtained a great popularity for solving differential and integral equations. From different wavelet families we consider here the Haar wavelets. Since the Haar wavelets are mathematically most simple to be compared with other wavelets, then interest to them is rapidly increasing and there is a great number of papers,where thesewavelets are used tor solving problems of calculus. An overview of such works can be found in the survey paper by Hariharan...

Locally supported orthogonal wavelet bases on the sphere via stereographic projection.

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