Approximate properties of methods of summability of Fourier integrals

Kotova, OV
Trigub, RM
Organization: 
Donbas National Academy of Civil Engineering and Architecture, Makiivka
Donetsk National University
Sumy State University
Dopov. Nac. akad. nauk Ukr. 2015, 1:13-19
https://doi.org/10.15407/dopovidi2015.01.013
Section: Mathematics
Language: Russian
Abstract: 
The exact orders of approximation of individual functions Rd → C by the classical methods of summability of Fourier integrals (Gauss–Weierstrass, Bochner–Riesz, Marcinkiewicz–Riesz) are determined.
Keywords: Bochner-Riesz, Gauss-Weierstrass, Marcinkiewicz-Riesz, summability of Fourier integrals
References: 
  1. Timan A. F. Theory of approximation of functions of a real variable, Moscow: Fizmathiz, 1960 (in Russian).
  2. Nikolskii S. M. Approximation of functions of several variables and embedding theorems, Moscow: Nauka, 1977 (in Russia).
  3. Trigub R. M. Izv. AN USSR. Ser. matem., 1965, 29, No 3: 615–630 (in Russian).
  4. Trigub R. M. Izv. AN USSR. Ser. matem., 1968, 32, No 1: 24–49 (in Russian).
  5. Trigub R. M. Izv. AN USSR. Ser. matem., 1980, 44, No 6: 1378–1409 (in Russian).
  6. Trigub R. M., Belinsky E. S. Fourier analysis and approximation of functions, Dordrecht: Kluwer, 2004. https://doi.org/10.1007/978-1-4020-2876-2
  7. Draganov B. R. J. Approxim. Theory., 2010, 162: 952–979.
  8. Shapiro H. S. Bull. Amer. Math. Soc. 1968, 74, No 3: 500–504. https://doi.org/10.1090/S0002-9904-1968-11980-9
  9. Stein I., Veis H. Introduction to Fourier analysis on Euclidean spaces, Moscow: Mir, 1974 (in Russian).
  10. Liflyand E., Samko S., Trigub R. Analysis and Math. Physics., 2012, 2, No 1: 1–68.
  11. Levin B.Ya. In: Transl. Math. Monogr. Vol. 150, Providence, R. I.: Amer. Math. Soc., 1996.
  12. Rathore R. K. S. J. Approxim. Theory., 1994, 77: 153–166.
  13. Bernshtein S. N. Dokl. AN USSR, 1947, 57, No 2: 111–114 (in Russian).
  14. Stechkin S. B. Izv. AN USSR. Ser. mat., 1951, 15, No 3: 219–242 (in Russian).
  15. Trihub R. M. Matem. sb., 2013, 204, No 12: 127–146 (in Russian).