Mixed Series of Jacobi and Chebyshev Polynomials and Their Discretization
Matematičeskie zametki, Tome 88 (2010) no. 1, pp. 116-147.

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This paper is devoted to the study of approximation properties of mixed series of Jacobi polynomials on weighted Sobolev spaces and of discretized mixed series of Chebyshev polynomials of the first kind from classes of analytic functions.
Mots-clés : Jacobi polynomial, Fourier–Jacobi series
Keywords: Chebyshev polynomial, weighted Sobolev space, analytic function, lebesgue inequality, ultraspherical polynomial.
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I. I. Sharapudinov; T. I. Sharapudinov. Mixed Series of Jacobi and Chebyshev Polynomials and Their Discretization. Matematičeskie zametki, Tome 88 (2010) no. 1, pp. 116-147. http://geodesic.mathdoc.fr/item/MZM_2010_88_1_a9/

[1] I. I. Sharapudinov, “Priblizhenie funktsii s peremennoi gladkostyu summami Fure–Lezhandra”, Matem. sb., 191:5 (2000), 143–160 | MR | Zbl

[2] I. I. Sharapudinov, “Smeshannye ryady po ultrasfericheskim polinomam i ikh approksimativnye svoistva”, Matem. sb., 194:3 (2003), 115–148 | MR | Zbl

[3] I. I. Sharapudinov, “Approksimativnye svoistva operatorov $\mathscr Y_{n+2r}(f)$ i ikh diskretnykh analogov”, Matem. zametki, 72:5 (2002), 765–795 | MR | Zbl

[4] I. I. Sharapudinov, Smeshannye ryady po ortogonalnym polinomam. Teoriya i prilozheniya, DNTs RAN, Makhachkala, 2004

[5] I. I. Sharapudinov, “Approksimativnye svoistva srednikh tipa Valle-Pussena chastichnykh summ smeshannogo ryada po polinomam Lezhandra”, Matem. zametki, 84:3 (2008), 452–471 | MR | Zbl

[6] G. Segë, Ortogonalnye mnogochleny, Fizmatgiz, M., 1962 | MR | Zbl

[7] S. A. Agakhanov, G. I. Natanson, “Funktsiya Lebega summ Fure–Yakobi”, Vestn. Leningr. un-ta. Ser. matem., mekh., astron., 1968, no. 1, 11–23 | MR | Zbl

[8] V. M. Badkov, “Otsenki funktsii Lebega i ostatka ryada Fure–Yakobi”, Sib. matem. zhurn., 9:6 (1968), 1263–1283 | MR | Zbl

[9] A. F. Timan, Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatgiz, M., 1960 | MR | Zbl

[10] I. I. Sharapudinov, “O nailuchshem priblizhenii i summakh Fure–Yakobi”, Matem. zametki, 34:5 (1983), 651–661 | MR | Zbl

[11] S. A. Telyakovskii, “Dve teoremy o priblizhenii funktsii algebraicheskimi mnogochlenami”, Matem. sb., 70:2 (1966), 252–265 | MR | Zbl

[12] I. E. Gopengauz, “K teoreme A. F. Timana o priblizhenii funktsii mnogochlenami na konechnom otrezke”, Matem. zametki, 1:2 (1967), 163–172 | MR | Zbl

[13] I. I. Sharapudinov, “Odnovremennoe priblizhenie funktsii i proizvodnykh, algebro-trigonometricheskie polinomy i smeshannye ryady po ortogonalnym polinomam”, Materialy konferentsii Voronezhskoi zimnei matematicheskoi shkoly “Sovremennye metody teorii funktsii i smezhnye problemy”, Izd.-poligraf. tsentr Voronezhsk. gos. un-ta, Voronezh, 2009, 189

[14] I. I. Sharapudinov, “O bazisnosti sistemy polinomov Lezhandra v prostranstve Lebega $L^{p(x)}(-1,1)$ s peremennym pokazatelem $p(x)$”, Matem. sb., 200:1 (2009), 137–160 | MR | Zbl

[15] I. K. Daugavet, Teoriya priblizhennykh metodov. Lineinye uravneniya, BVKh-Peterburg, SPb, 2006

[16] S. Pashkovskii, Vychislitelnye primeneniya mnogochlenov i ryadov Chebysheva, Nauka, M., 1983 | MR | Zbl

[17] R. Haverkamp, “Approximationsfehler der Ableitungen von Interpolationspolynomen”, J. Approx. Theory, 30:3 (1980), 180–196 | DOI | MR | Zbl

[18] T. W. Tee, L. N. Trefethen, “A rational spectral collocation method with adaptively transformed Chebyshev grid points”, SIAM J. Sci. Comput., 28:5 (2006), 1798–1811 | DOI | MR | Zbl

[19] B. Muckenhoupt, “Mean convergence of Jacobi series”, Proc. Amer. Math. Soc., 23:2 (1969), 306–310 | DOI | MR | Zbl

[20] A. Zigmund, Trigonometricheskie ryady, v. 1, 2, Mir, 1965 | MR | Zbl | Zbl