caa a22 4500 605523428 CHVBK 20210128100749.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10958-015-2623-y doi (NATIONALLICENCE)springer-10.1007/s10958-015-2623-y Approximative properties of the summation methods of Fourier integrals [Elektronische Daten] [Ol'ga Kotova, Roald Trigub] We study the order (velocity) of the approximation of functions on the axis by entire functions of exponential type not higher than σ as σ → ∞ (the linear and best approximations). The exact order of approximation of individual functions on ℝ d by the classical summation methods of Fourier integrals (Gauss-Weierstrass, Bochner-Riesz, Marcinkiewicz) and the nonclassical Bernstein-Stechkin method is found. For functions on a torus, similar theorems of approximation by polynomials were obtained previously. Springer Science+Business Media New York, 2015 Entire functions of exponential type nationallicence Bernstein-Riesz inequality nationallicence algebra of absolutely convergent Fourier integrals nationallicence summation methods nationallicence modulus of smoothness nationallicence K -functional nationallicence Fourier multiplier nationallicence total variation of a measure nationallicence Kotova Ol'ga Donbas National Academy of Building and Architecture, Donetsk, Ukraine aut Trigub Roald Sumy State University, Sumy, Ukraine aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 211/5(2015-12-01), 668-683 1072-3374 211:5<668 2015 211 10958 https://doi.org/10.1007/s10958-015-2623-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2623-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kotova Ol'ga Donbas National Academy of Building and Architecture, Donetsk, Ukraine aut NATIONALLICENCE 700 1- Trigub Roald Sumy State University, Sumy, Ukraine aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 211/5(2015-12-01), 668-683 1072-3374 211:5<668 2015 211 10958