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Biquadratic splines interpolating mean values

Jiří Kobza, Jan Mlčák (1994)

Applications of Mathematics

Continuity conditions for a biquadratic spline interpolating given mean values in terms of proper parameters are given. Boundary conditions determining such a spline and the algorithm for computing local parameters for the given data are studied. The notion of the natural spline and its extremal property is mentioned.

BMO and Lipschitz approximation by solutions of elliptic equations

Joan Mateu, Yuri Netrusov, Joan Orobitg, Joan Verdera (1996)

Annales de l'institut Fourier

We consider the problem of qualitative approximation by solutions of a constant coefficients homogeneous elliptic equation in the Lipschitz and BMO norms. Our method of proof is well-known: we find a sufficient condition for the approximation reducing matters to a weak * spectral synthesis problem in an appropriate Lizorkin-Triebel space. A couple of examples, evolving from one due to Hedberg, show that our conditions are sharp.

Box-spline histograms for multivariate density estimation

Karol Dziedziul, Piotr Paluszek (2010)

Applicationes Mathematicae

The uniform approach to calculation of MISE for histogram and density box-spline estimators gives us a possibility to obtain estimators of derivatives of densities and the asymptotic constant.

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