Polynomials orthogonal with sign-sensitive weight
Matematičeskie zametki, Tome 59 (1996) no. 5, pp. 737-752.

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

We introduce the notion of inner product with sign-sensitive weight and construct systems of nonsymmetrically orthonormalized polynomials. We also study some properties of such polynomials (for example, the properties of Fourier coefficients, quadrature formulas of Gauss type, etc.).
@article{MZM_1996_59_5_a9,
     author = {A. K. Ramazanov},
     title = {Polynomials orthogonal with sign-sensitive weight},
     journal = {Matemati\v{c}eskie zametki},
     pages = {737--752},
     publisher = {mathdoc},
     volume = {59},
     number = {5},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_5_a9/}
}
TY  - JOUR
AU  - A. K. Ramazanov
TI  - Polynomials orthogonal with sign-sensitive weight
JO  - Matematičeskie zametki
PY  - 1996
SP  - 737
EP  - 752
VL  - 59
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_59_5_a9/
LA  - ru
ID  - MZM_1996_59_5_a9
ER  - 
%0 Journal Article
%A A. K. Ramazanov
%T Polynomials orthogonal with sign-sensitive weight
%J Matematičeskie zametki
%D 1996
%P 737-752
%V 59
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1996_59_5_a9/
%G ru
%F MZM_1996_59_5_a9
A. K. Ramazanov. Polynomials orthogonal with sign-sensitive weight. Matematičeskie zametki, Tome 59 (1996) no. 5, pp. 737-752. http://geodesic.mathdoc.fr/item/MZM_1996_59_5_a9/

[1] Dolzhenko E. P., Sevastyanov E. A., “Znakochuvstvitelnye approksimatsii. Prostranstvo znakochuvstvitelnykh vesov. Zhestkost i svoboda sistemy”, Dokl. RAN, 332:6 (1993), 686–689 | Zbl

[2] Dolzhenko E. P., Sevastyanov E. A., “Znakochuvstvitelnye approksimatsii. Voprosy edinstvennosti i ustoichivosti”, Dokl. RAN, 333:1 (1993), 5–7 | Zbl

[3] Babenko V. F., “Nesimmetrichnye priblizheniya v prostranstvakh summiruemykh funktsii”, UMZh, 34:4 (1982), 409–416 | MR | Zbl

[4] Suetin P. K., Klassicheskie ortogonalnye polinomy, Nauka, M., 1976

[5] Segë G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[6] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974