On Bernstein classes of well approximable maps

• Alexander Brudnyi ^[1]
  1. [1] University of Calgary

     University of Calgary

     Canadá

     
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 200, Nº 1 (December 2015), 2015, págs. 259-293
• Idioma: inglés
• DOI: 10.1016/j.jat.2015.08.004
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• Resumen

  • We study the structure of families of “well approximable” elements of tensor products of Banach spaces including analogs of the classical quasianalytic classes in the sense of Bernstein and Beurling. As in the case of quasianalytic functions, we prove for members of these families variants of the Mazurkiewicz and Markushevich theorems and in some particular cases, if such elements are Banach-valued continuous maps on a compact metric space, estimate massivity of their graphs and level sets.