Abstract
Shape-preserving properties of some naturally arising bivariate wavelet operators B n are presented. Namely, let \(f\in C^{k}(\mathbb{R}\mathrm{ ^{2}}),\ k>0,\ r,s\geq 0\) all integers such that r + s = k. If
then it is established, under mild conditions on B n , that
also pointwise convergence of B n (f) to f is given with rates through a Jackson type inequality. Related simultaneous shape-preserving results are also given for special type of wavelet operators B n . This chapter relies on [89].
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© 2011 Springer-Verlag Berlin Heidelberg
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Anastassiou, G.A. (2011). Bidimensional Constrained Wavelet Like Approximation. In: Intelligent Mathematics: Computational Analysis. Intelligent Systems Reference Library, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17098-0_3
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DOI: https://doi.org/10.1007/978-3-642-17098-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17097-3
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