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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2018 Volume 58, Number 10, Pages 1596–1603 (Mi zvmmf10787)

Sharp estimates for the convergence rate of Fourier series in two variables and their applications

F. V. Abilovaa, E. V. Selimkhanovb

a Dagestan State Technical University, Makhachkala, Russia
b Dagestan State University, Makhachkala, Russia

Abstract: Sharp estimates for the convergence rate of Fourier series with respect to the trigonometric system for functions of two variables characterized by a generalized modulus of continuity are given.

Key words: Fourier series, generalized modulus of continuity, spherical, rhombic, and hyperbolic sums, $N$-width, cubature formula.

UDC: 519.651

Received: 01.09.2017

DOI: 10.31857/S004446690003580-9


 English version:
Computational Mathematics and Mathematical Physics, 2018, 58:10, 1545–1551

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© Steklov Math. Inst. of RAS, 2024