Geodesic
Discrete polynomials orthogonal with respect Sobolev-type inner product associated with Chebyshev polynomials orthogonal on a uniform grid
Daghestan Electronic Mathematical Reports, Tome 4 (2015), pp. 15-20.

Voir la notice de l'article provenant de la source Math-Net.Ru

In current paper we consider new polynomials, generated by orthogonal on uniform grid Chebyshev polynomials. Newly introduced polynomials are themselves orthogonal with respect to the Sobolev-type inner product. The explicit form of these polynomials, convenient to study their asymptotic properties, is obtained.
Keywords: orthogonal polynomials, Sobolev-type orthogonal polynomials, Chebyshev polynomials. 
@article{DEMR_2015_4_a1,
     author = {T. I. Sharapudinov},
     title = {Discrete polynomials orthogonal with respect {Sobolev-type} inner product associated with {Chebyshev} polynomials orthogonal on a uniform grid},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {15--20},
     publisher = {mathdoc},
     volume = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2015_4_a1/}
}
TY  - JOUR
AU  - T. I. Sharapudinov
TI  - Discrete polynomials orthogonal with respect Sobolev-type inner product associated with Chebyshev polynomials orthogonal on a uniform grid
JO  - Daghestan Electronic Mathematical Reports
PY  - 2015
SP  - 15
EP  - 20
VL  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DEMR_2015_4_a1/
LA  - ru
ID  - DEMR_2015_4_a1
ER  - 
%0 Journal Article
%A T. I. Sharapudinov
%T Discrete polynomials orthogonal with respect Sobolev-type inner product associated with Chebyshev polynomials orthogonal on a uniform grid
%J Daghestan Electronic Mathematical Reports
%D 2015
%P 15-20
%V 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DEMR_2015_4_a1/
%G ru
%F DEMR_2015_4_a1
T. I. Sharapudinov. Discrete polynomials orthogonal with respect Sobolev-type inner product associated with Chebyshev polynomials orthogonal on a uniform grid. Daghestan Electronic Mathematical Reports, Tome 4 (2015), pp. 15-20. http://geodesic.mathdoc.fr/item/DEMR_2015_4_a1/

[1] Kwon K.H., Littlejohn L.L., “The orthogonality of the Laguerre polynomials $\{L_n^{(-k)}(x)\}$ for positive integers $k$”, Ann. Numer. Anal., 2 (1995), 289–303 | MR | Zbl

[2] Kwon K.H., Littlejohn L.L., “Sobolev orthogonal polynomials and second-order differential equations”, Rocky Mountain J. Math., 1998, 547–594 | DOI | MR | Zbl

[3] Marcellan F., Alfaro M., Rezola M.L., “Orthogonal polynomials on Sobolev spaces: old and new directions”, Journal of Computational and Applied Mathematics, 48 (1993), 113–131 | DOI | MR | Zbl

[4] Iserles A., Koch P.E., Norsett S.P., Sanz-Serna J.M., “On polynomials orthogonal with respect to certain Sobolev inner products”, J. Approx. Theory, 65 (1991), 151–175 | DOI | MR | Zbl

[5] Meijer H.G., “Laguerre polynomials generalized to a certain discrete Sobolev inner product space”, J. Approx. Theory, 73 (1993), 1–16 | DOI | MR | Zbl

[6] Marcellan F., Yuan Xu, On Sobolev orthogonal polynomials, 25 Mar 2014, 40 pp., arXiv: 1403.6249v1 [math.CA]

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

[8] Sharapudinov I.I., “Approksimativnye svoistva operatorov ${\cal Y}_{n+2r}(f)$ i ikh diskretnykh analogov”, Matematicheskie zametki, 72:5 (2002), 765–795 | DOI | MR | Zbl

[9] Sharapudinov I.I., Smeshannye ryady po ortogonalnym polinomam, Izdatelstvo Dagestanskogo nauchnogo tsentra, Makhachkala, 2004, 176 pp.

[10] Sharapudinov I.I., “Smeshannye ryady po polinomam Chebysheva, ortogonalnym na ravnomernoi setke”, Matematicheskie zametki, 78:3 (2005), 442–465 | DOI | MR | Zbl

[11] Sharapudinov I.I., “Approksimativnye svoistva smeshannykh ryadov po polinomam Lezhandra na klassakh $W^r$”, Matematicheskii sbornik, 197:3 (2006), 135–154 | DOI | MR | Zbl

[12] Sharapudinov I.I., “Approksimativnye svoistva srednikh tipa Valle-Pussena chastichnykh summ smeshannykh ryadov po polinomam Lezhandra”, Matematicheskie zametki, 197:3 (2008), 452–471 | DOI

[13] Chebyshev P.L., “O nepreryvnykh drobyakh (1855)”, Poln. sobr. soch., v. 2, Izd. AN SSSR, M., 1947, 103–126 | MR

[14] Chebyshev P.L., “Ob odnom novom ryade”, Poln. sobr. soch., v. 2, Izd. AN SSSR, M., 1947, 236–238 | MR

[15] Chebyshev P.L., “Ob interpolirovanii po sposobu naimenshikh kvadratov (1859)”, Poln. sobr. soch., v. 2, Izd. AN SSSR, M., 1947, 314–334 | MR

[16] Chebyshev P.L., “Ob interpolirovanii (1864)”, Poln. sobr. soch., v. 2, Izd. AN SSSR, M., 1947, 357–374 | MR

[17] Chebyshev P.L., “Ob interpolirovanii velichin ravnootstoyaschikh (1875)”, Poln. sobr. soch., v. 2, Izd. AN SSSR, M., 1947, 66–87 | MR

[18] Sharapudinov I.I., Mnogochleny, ortogonalnye na setkakh, Izdatelstvo Dag. gos. ped. un-ta, Makhachkala, 1997, 252 pp.

[19] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, Moskva, 1962, 500 pp.