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@article{MZM_2010_88_1_a9, author = {I. I. Sharapudinov and T. I. Sharapudinov}, title = {Mixed {Series} of {Jacobi} and {Chebyshev} {Polynomials} and {Their} {Discretization}}, journal = {Matemati\v{c}eskie zametki}, pages = {116--147}, publisher = {mathdoc}, volume = {88}, number = {1}, year = {2010}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_1_a9/} }
TY - JOUR AU - I. I. Sharapudinov AU - T. I. Sharapudinov TI - Mixed Series of Jacobi and Chebyshev Polynomials and Their Discretization JO - Matematičeskie zametki PY - 2010 SP - 116 EP - 147 VL - 88 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2010_88_1_a9/ LA - ru ID - MZM_2010_88_1_a9 ER -
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