Geodesic
On the Order of Convergence of Quadrature Formulae on Functions in the Spaces of Riesz Potential
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 3, pp. 296-307

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

We establish an unimprovable lower estimate for the errors of quadrature formulae with no restrictions on nodes and coefficients with integrating the Riesz potentials.
Mots-clés : quadrature formulas
Keywords: error functionals, sequences of functionals, Riesz potential. 
Mariya I. Medvedeva. On the Order of Convergence of Quadrature Formulae on Functions in the Spaces of Riesz Potential. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 3, pp. 296-307. http://geodesic.mathdoc.fr/item/JSFU_2008_1_3_a8/
@article{JSFU_2008_1_3_a8,
     author = {Mariya I. Medvedeva},
     title = {On the {Order} of {Convergence} of {Quadrature} {Formulae} on {Functions} in the {Spaces} of {Riesz} {Potential}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {296--307},
     year = {2008},
     volume = {1},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2008_1_3_a8/}
}
TY  - JOUR
AU  - Mariya I. Medvedeva
TI  - On the Order of Convergence of Quadrature Formulae on Functions in the Spaces of Riesz Potential
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2008
SP  - 296
EP  - 307
VL  - 1
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JSFU_2008_1_3_a8/
LA  - ru
ID  - JSFU_2008_1_3_a8
ER  - 
%0 Journal Article
%A Mariya I. Medvedeva
%T On the Order of Convergence of Quadrature Formulae on Functions in the Spaces of Riesz Potential
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2008
%P 296-307
%V 1
%N 3
%U http://geodesic.mathdoc.fr/item/JSFU_2008_1_3_a8/
%G ru
%F JSFU_2008_1_3_a8

[1] V. I. Polovinkin, “Posledovatelnosti funktsionalov s pogranichnym sloem v prostranstvakh odnomernykh funktsii, obladayuschikh drobnymi proizvodnymi Rimana–Liuvillya”, Matematicheskie trudy, 5:2 (2002), 178–202 | MR | Zbl

[2] N. A. Sevastyanova, “Posledovatelnosti funktsionalov s pogranichnym sloem dlya funktsii, imeyuschikh drobnye proizvodnye”, Kubaturnye formuly i ikh prilozheniya, IMVTs UfNTs RAN, Ufa, 1996, 90–104

[3] N. A. Sevastyanova, “Posledovatelnosti funktsionalov s pogranichnym sloem v prostranstvakh funktsii s drobnymi proizvodnymi”, Voprosy matematicheskogo analiza, 2, IPTs KGTU, Krasnoyarsk, 1997, 106–119

[4] L. B. Samko, A. A. Kilbas, O. I. Marichev, Integraly i proizvodnye drobnogo poryadka i nekotorye ikh primeneniya, Nauka i tekhnika, Minsk, 1987 | Zbl

[5] M. I. Medvedeva, “Asimptotika norm funktsionalov oshibok s pogranichnym sloem dlya potentsialov Rissa”, Voprosy matematicheskogo analiza, 8, IPTs KGTU, Krasnoyarsk, 2004, 85–98

[6] V. I. Polovinkin, Kvadraturnye formuly v prostranstvakh funktsii, SFU, Krasnoyarsk, 2007

[7] F. D. Gakhov, Kraevye zadachi, Nauka, M., 1977 | MR | Zbl

[8] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady, Nauka, M., 1981 | MR | Zbl