Geodesic
On the Representation of Sobolev Systems Orthogonal with Respect to the Inner Product with One Discrete Point
Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 561-570 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We obtain the representation of systems of functions $\Phi_1$ orthogonal with respect to the Sobolev-type inner product with one discrete point in terms of functions of systems orthogonal in $L^2$. Questions relating to the completeness of the system $\Phi_1$ are investigated. Some properties of systems of functions obtained by differentiating the system $\Phi_1$ are studied.
Keywords: Sobolev orthogonality, completeness of orthogonal systems, representation of Sobolev systems, differentiation of Sobolev systems. 
@article{MZM_2022_111_4_a7,
     author = {M. G. Magomed-Kasumov and T. N. Shakh-Emirov},
     title = {On the {Representation} of {Sobolev} {Systems} {Orthogonal} with {Respect} to the {Inner} {Product} with {One} {Discrete} {Point}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {561--570},
     year = {2022},
     volume = {111},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a7/}
}
TY  - JOUR
AU  - M. G. Magomed-Kasumov
AU  - T. N. Shakh-Emirov
TI  - On the Representation of Sobolev Systems Orthogonal with Respect to the Inner Product with One Discrete Point
JO  - Matematičeskie zametki
PY  - 2022
SP  - 561
EP  - 570
VL  - 111
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a7/
LA  - ru
ID  - MZM_2022_111_4_a7
ER  - 
%0 Journal Article
%A M. G. Magomed-Kasumov
%A T. N. Shakh-Emirov
%T On the Representation of Sobolev Systems Orthogonal with Respect to the Inner Product with One Discrete Point
%J Matematičeskie zametki
%D 2022
%P 561-570
%V 111
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a7/
%G ru
%F MZM_2022_111_4_a7
M. G. Magomed-Kasumov; T. N. Shakh-Emirov. On the Representation of Sobolev Systems Orthogonal with Respect to the Inner Product with One Discrete Point. Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 561-570. http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a7/

[1] F. Marcellán, Y. Xu, “On Sobolev orthogonal polynomials”, Expo Math, 33:3 (2015), 308–352 | DOI | MR | Zbl

[2] I. I. Sharapudinov, “Sistemy funktsii, ortogonalnye po Sobolevu, assotsiirovannye s ortogonalnoi sistemoi”, Izv. RAN. Ser. matem., 82:1 (2018), 225–258 | DOI | MR | Zbl

[3] I. I. Sharapudinov, “Ortogonalnye po Sobolevu sistemy funktsii i nekotorye ikh prilozheniya”, UMN, 74:4 (448) (2019), 87–164 | DOI | MR | Zbl