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Universally optimal approximation of functionals

Milan Práger (1979)

Aplikace matematiky

A universal optimal in order approximation of a general functional in the space of continuous periodic functions is constructed and its fundamental properties and some generalizations are investigated. As an application the approximation of singular integrals is considered and illustrated by numerical results.

ε-Entropy and moduli of smoothness in L p -spaces

A. Kamont (1992)

Studia Mathematica

The asymptotic behaviour of ε-entropy of classes of Lipschitz functions in L p ( d ) is obtained. Moreover, the asymptotics of ε-entropy of classes of Lipschitz functions in L p ( d ) whose tail function decreases as O ( λ - γ ) is obtained. In case p = 1 the relation between the ε-entropy of a given class of probability densities on d and the minimax risk for that class is discussed.

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