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A note on best n-term approximation for generalized Wiener classes

Ronald DeVore, Guergana Petrova, Przemyslaw Wojtaszczyk

Abstract

We determine the best n-term approximation of generalized Wiener model classes in a Hilbert space $H $. This theory is then applied to several special cases.

A note on best n-term approximation for generalized Wiener classes

Abstract

We determine the best n-term approximation of generalized Wiener model classes in a Hilbert space . This theory is then applied to several special cases.
Paper Structure (3 sections, 4 theorems, 48 equations)

This paper contains 3 sections, 4 theorems, 48 equations.

Table of Contents

  1. Introduction
  2. Best $n$ term approximation for $U(\ell_p({\bf w}))$
  3. Special cases of sequence spaces

Key Result

Lemma 2.1

If ${\bf x}\in \ell_p({\bf w})$, then ${\bf x}^*\in \ell_p({\bf w})$ , $\sigma_n({\bf x})=\sigma_n({\bf x}^*)$, and

Theorems & Definitions (9)

  • Lemma 2.1
  • proof
  • Theorem 2.2
  • proof
  • Corollary 3.1
  • proof
  • Corollary 3.2
  • proof
  • Remark 3.3