On Two Problems in the Multivariate Approximation
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SOUTH CAROLINA UNIV COLUMBIA COLUMBIA
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The paper contains two theorems on approximation of functions with bounbed mixed derivative. These theorems give some progress in two old open problems. The first one gives, in particular, an upper estimate in the Bernstein Lsub 1-inequality for trigonometric polynomials on two variables with harmonics in hyperbolic crosses. The second one gives the order of the entropy numbers and Kolmogorovs widths in the L infinity-norm of the class MWr infinity,alpha of functions of two variables.
- Numerical Mathematics