On a Norm and Approximate Characteristics of Classes of Multivariable Functions

B. S. Kashin ; V. N. Temlyakov

Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 58-79.

Résumé

We introduce a space of quasicontinuous functions and study its approximate characteristics, i.e., $\varepsilon$-entropy and widths. We establish inequalities for norms of trigonometric polynomials in this space. Besides, we obtain exponents of $\varepsilon$-entropy and widths of some classes of functions with low smoothness.

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