Geodesic
Convergence of Fourier sums by polynomials orthogonal on arbitrary lattice
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2012), pp. 60-62.

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We study approximation properties of discrete Fourier sums of a function on the segment $[-1,1]$ on an orthonormal system of polynomials representing finite-difference analogs of classical Legendre polynomials. In particular, we find an order of the norm of discrete Fourier sum.
Mots-clés : polynomial
Keywords: orthogonal system, lattice, weight, weight estimate, asymptotic formula, approximation, Fourier sums. 
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A. A. Nurmagomedov. Convergence of Fourier sums by polynomials orthogonal on arbitrary lattice. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2012), pp. 60-62. http://geodesic.mathdoc.fr/item/IVM_2012_7_a7/

[1] Nurmagomedov A. A., “Ob asimptotike mnogochlenov, ortogonalnykh na proizvolnykh setkakh”, Izv. Saratovsk. un-ta. Nov. ser. Ser. Matem., mekhan., informatika, 8:1 (2008), 25–31

[2] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[3] Rau H., “Über die Lebesgueschen Konstanten der Reihenentwicklungen nach Jacobischen Polynomen”, J. fur Math., 161 (1929), 237–254 | Zbl

[4] Gronwall T., “Über die Laplacesche Reihe”, Math. Ann., 74:2 (1913), 213–270 | DOI | MR | Zbl

[5] Agakhanov S. A., Natanson G. I., “Priblizhenie funktsii summami Fure–Yakobi”, DAN SSSR, 166:1 (1966), 9–10 | Zbl

[6] Agakhanov S. A., Natanson G. I., “Funktsiya Lebega summ Fure–Yakobi”, Vestn. Leningradsk. un-ta, 1968, no. 1, 11–13

[7] Sharapudinov I. I., “O skhodimosti metoda naimenshikh kvadratov”, Matem. zametki, 53:3 (1993), 131–143 | MR | Zbl

[8] Korkmasov F. M., “Approksimativnye svoistva srednikh Valle-Pussena dlya diskretnykh summ Fure–Yakobi”, Sib. mat. zhurn., 45:2 (2004), 334–355 | MR | Zbl

[9] Badkov V. M., “Otsenki funktsii Lebega i ostatka ryada Fure–Yakobi”, Sib. matem. zhurn., 9:6 (1978), 1263–1283 | MR

[10] Aleksich G., Problemy skhodimosti ortogonalnykh ryadov, In. lit., M., 1963 | MR

[11] Badkov V. M., “Dvustoronnie otsenki funktsii Lebega i ostatka ryada Fure po ortogonalnym mnogochlenam”, Approksimatsiya v konkretnykh i abstraktnykh banakhovykh prostranstvakh, sb., AN SSSR, Uralsk. nauchn. tsentr, Sverdlovsk, 1987, 31–45 | MR

[12] Shakirov I. A., “Polnoe issledovanie funktsii Lebega, sootvetstvuyuschikh klassicheskim interpolyatsionnym polinomam Lagranzha”, Izv. vuzov. Matem., 2011, no. 10, 80–88 | MR | Zbl