The Marcinkiewicz-type discretization theorems for the hyperbolic cross polynomials

• V. N. Temlyakov ^[1]
  1. [1] University of South Carolina

     University of South Carolina

     Estados Unidos

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 9, Nº. 1-2, 2017, págs. 37-63
• Idioma: inglés
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• Resumen

  • The main goal of this paper is to study the discretization problem for the hyperbolic cross trigonometric polynomials. This important problem turns out to be very difficult. In this paper we begin a systematic study of this problem and demonstrate two different techniques – the probabilistic and the number theoretical techniques.