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Article
On density of interpolation points, a Kadec-type theorem, and Saff's principle of contamination inL p-approximation
Letf ∈L p (I) and denote byB n,p (f) the polynomial of bestL p-approximation tof of degreen (1<p<∞,I=[−1,1], the norm is weightedL p-norm with an arbitrary positive weight). Ex...
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Article
Local Lipschitz constants and Kolushov polynomials
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Energy Transfer in Cr, Tm:YAG
We describe a systematic analysis of energy transfer processes in crystals of YAG doped with varying concentrations of Cr and Tm. We use both spectral measurements and measurements of the temporal response to ...
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Article
Best monotone approximation and the Hardy-Littlewood maximal function
If f∈L2[0, 1] and g*∈L2[0, 1] is the best non-decreasing approximation to f, then it's shown that ‖f−g*‖2=‖f−θ(f)‖2, where θ(f) denotes the Hardy-Littlewood maximal function of f.
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Article
Construction of a best monotone approximation in Ip for 1<p<∞
In this paper we present a construction of the best lp monotone approximation for 1<p<∞.
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Article
Limits of strong unicity constants for certainC ∞ functions
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Article
On a class of non-linear filtration laws
Non-linear filtration is of considerable practical importance, since it arises, in particular, in connection with oil drilling operations. Thus, for example, flows of paraffin-based oils, of oils containing as...