Displaying similar documents to “Cauchy's functional equation in restricted complex domains.”

On some BK spaces.

De Malafosse, Bruno (2003)

International Journal of Mathematics and Mathematical Sciences

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Representation formulae for (C₀) m-parameter operator semigroups

Mi Zhou, George A. Anastassiou (1996)

Annales Polonici Mathematici

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Some general representation formulae for (C₀) m-parameter operator semigroups with rates of convergence are obtained by the probabilistic approach and multiplier enlargement method. These cover all known representation formulae for (C₀) one- and m-parameter operator semigroups as special cases. When we consider special semigroups we recover well-known convergence theorems for multivariate approximation operators.

Distortion mismatch in the quantization of probability measures

Siegfried Graf, Harald Luschgy, Gilles Pagès (2008)

ESAIM: Probability and Statistics

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We elucidate the asymptotics of the -quantization error induced by a sequence of -optimal -quantizers of a probability distribution on d when . In particular we show that under natural assumptions, the optimal rate is preserved as long as (and for every in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based cubature formulae in numerical integration on d and on the Wiener space.