The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator on is proved. In this note there is shown that in the cases , no other transforms of this kind exist and for case , all such transforms are described.
We present here some details of our implementation of Wavelet-Galerkin method for Poisson equation in C language parallelized by POSIX threads library and show its performance in dimensions .
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.
In signal and image processing as well as in numerical solution of differential equations, wavelets with short support and with vanishing moments are important because they have good approximation properties and enable fast algorithms. A B-spline of order is a spline function that has minimal support among all compactly supported refinable functions with respect to a given smoothness. And recently, B. Han and Z. Shen constructed Riesz wavelet bases of with vanishing moments based on B-spline...
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