The Marcinkiewicz-type discretization theorems for the hyperbolic cross polynomials
arXiv:1702.0161741 citations
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It provides foundational results for discretization of hyperbolic cross polynomials, which is important for approximation theory and numerical analysis.
The paper studies the discretization problem for hyperbolic cross trigonometric polynomials, presenting two techniques (probabilistic and number-theoretic) to address this difficult problem.
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.