PHYSICS AND MATHEMATICS

Estimation of the best approximation of the spectrum of the hyperbolic crosses

M. E. Turova

Al-Farabi Kazakh National University

Abstract: The article describes the process of getting a new accurate estimate of the best approximation by trigonometric polynomials range “type of hyperbolic crosses” in the Besov space, through the use of known and proven assessment results. The range approximating polynomials lies in the set generated by the level surfaces of the function $\Omega(t)$. These sets are a generalization of hyperbolic crosses to arbitrary $\Omega(t)$.

Keywords: the best approximation, assessment of best approximation, modulus of smoothness, modulus of continuity, hyperbolic cross.

UDC: 51

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