Approximation by polynomials with only real critical points

• David L. Bishop ^[1]
  1. [1] Yale University

     Yale University

     Town of New Haven, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 6, 2024, págs. 2251-2290
• Idioma: inglés
• DOI: 10.4171/RMI/1470
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• Resumen

  • We strengthen the Weierstrass approximation theorem by proving that any real-valued continuous function on an interval I⊂R can be uniformly approximated by a real-valued polynomial whose only (possibly complex) critical points are contained in I. The proof uses a perturbed version of the Chebyshev polynomials and an application of the Brouwer fixed point theorem