Order estimates of the best $n$-term orthogonal trigonometric approximations of the classes ${\cal F}_{q}^{\psi}$ of periodic functions in the integral metrics

TL;DR

This paper derives order estimates for the best n-term orthogonal trigonometric approximations of certain classes of periodic functions in Lp spaces, focusing on functions with rapidly decreasing Fourier coefficients.

Contribution

It provides new order estimates for both optimal and greedy n-term approximations of classes with super-polynomial Fourier decay in Lp spaces.

Findings

Order estimates for best n-term orthogonal approximations in Lp.

Order estimates for n-term greedy approximations.

Applicable to classes with Fourier coefficients decreasing faster than any power.

Abstract

We obtain order estimates in the spaces $L_p$ of the best $n$-term trigonometric orthogonal approximations of the classes ${\cal F}_{q}^{\psi}$ of periodic functions, whose Fourier coefficients decrease faster then any power function. We also obtain order estimates of the quantities of approximations by $n$-term Greedy approximants of such classes in the spaces $L_p$.