On Optimal Recovery of the Operator of \(k\)-th Divided Difference From its Inaccurately Given Fourier Transform

For citation: Unuchek S. A. On Optimal Recovery of  the  Operator of \(k\)-th Divided Difference From its Inaccurately Given Fourier Transform. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 17, no. 3, pp.84-92. DOI 10.23671/VNC.2017.3.7268

1. Smoljak S. A. Ob Optimal'nom Vosstanovlenii Funkcij i
Funkcionalov ot Nih: Dis. … Kand. Fiz.-Mat. Nauk, M., MGU, 1965
(Russian).

2. Kolmogorov A. N. Izbrannye Trudy. Matematika i Mehanika, M.,
Nauka, 1985, 470 p (Russian).

3. Nikol'skij S. M. Concerning estimation for approximate quadrature
formulas. Uspehi Mat. Nauk (N.S.) [Russian Mathematical Surveys],
1950, vol. 5, no. 2(36), pp. 165-177 (Russian).

4. Marchuk A. G., Osipenko K. Ju. Best approximation of functions
specified with an error at a finite number of points. Math. Notes of
the Academy of Sciences of the USSR [Mat. Zametki, 1975, vol. 17,
no. 3, pp. 359-368], 1975, vol. 17, no. 3, pp. 207-212.

5. Unuchek S. A. Optimal reconstruction of divided differences from
an inaccurate sequence. Differential Equations [Dif. Uravnenija,
2015, vol. 51, no. 7, pp. 951-957], 2015, vol. 51, no. 7, pp.
948-954.

6. Magaril-Il'jaev G. G., Osipenko K. Ju. Optimal Recovery of
Functions and Their Derivatives from Inaccurate Information about
the Spectrum and Inequalities for Derivatives. Functional Analysis
and Its Applications [Funktsional. Anal. i Prilozhen., 2003, vol.
37, no. 3, pp. 51-64], 2003, vol. 37, no. 3, pp. 203-214.

7. Magaril-Il'jaev G. G., Osipenko K. Ju. The Hardy-Littlewood-Paley
inequality and the reconstruction of derivatives from inaccurate
data. Dokl. Math. [Dokl. Akad. Nauk, 2011, vol. 438, no. 3, pp.
300-302], 2011, vol. 83, no. 3, pp. 337-339.