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Abstract <p> We consider the problem of approximation of a continuous function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(f\)</EquationSource> </InlineEquation> defined on a compact metric space <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(X\)</EquationSource> </InlineEquation> by elements from a sum of two algebras. We prove a de la Vallée Poussin type theorem, which estimates the approximation error <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(E(f)\)</EquationSource> </InlineEquation> from below. We also obtain a duality formula for the precise computation of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(E(f)\)</EquationSource> </InlineEquation>. </p>

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A Note on the Approximation by a Sum of Two Algebras

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • A. Kh. Asgarova,
  • V. E. Ismailov

摘要

Abstract

We consider the problem of approximation of a continuous function \(f\) defined on a compact metric space \(X\) by elements from a sum of two algebras. We prove a de la Vallée Poussin type theorem, which estimates the approximation error \(E(f)\) from below. We also obtain a duality formula for the precise computation of \(E(f)\) .