Best “Continuous” $n$-Term Approximations in the Spaces $S_\phi ^p$

Abstract

We find exact values of upper bounds for the best approximations of $q$-ellipsoids by polynomials of degree $n$ in the spaces $S_\phi ^p$ in the case where the approximating polynomials are constructed on the basis of $n$-dimensional subsystems chosen successively from a given orthonormal system ϕ.