Geodesic
Absolute and Uniform Convergence of Eigenfunction Expansions of Integral Operators with Kernels Admitting Derivative Discontinuities on the Diagonals
Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 713-723 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An analog of Szasz's theorem on the absolute convergence of trigonometric Fourier series is established for expansions in the eigen and associated functions of integral operators some of whose kernels involve derivatives with discontinuities on the diagonals.
Keywords: integral operator, trigonometric Fourier series, Fredholm resolvent, Szasz's theorem on absolute convergence, boundary-value problem, modulus of continuity. 
@article{MZM_2007_81_5_a8,
     author = {V. V. Kornev},
     title = {Absolute and {Uniform} {Convergence} of {Eigenfunction} {Expansions} of {Integral} {Operators} with {Kernels} {Admitting} {Derivative} {Discontinuities} on the {Diagonals}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {713--723},
     year = {2007},
     volume = {81},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a8/}
}
TY  - JOUR
AU  - V. V. Kornev
TI  - Absolute and Uniform Convergence of Eigenfunction Expansions of Integral Operators with Kernels Admitting Derivative Discontinuities on the Diagonals
JO  - Matematičeskie zametki
PY  - 2007
SP  - 713
EP  - 723
VL  - 81
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a8/
LA  - ru
ID  - MZM_2007_81_5_a8
ER  - 
%0 Journal Article
%A V. V. Kornev
%T Absolute and Uniform Convergence of Eigenfunction Expansions of Integral Operators with Kernels Admitting Derivative Discontinuities on the Diagonals
%J Matematičeskie zametki
%D 2007
%P 713-723
%V 81
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a8/
%G ru
%F MZM_2007_81_5_a8
V. V. Kornev. Absolute and Uniform Convergence of Eigenfunction Expansions of Integral Operators with Kernels Admitting Derivative Discontinuities on the Diagonals. Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 713-723. http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a8/

[1] A. P. Khromov, “Ob obraschenii integralnykh operatorov s yadrami, razryvnymi na diagonalyakh”, Matem. zametki, 64:6 (1998), 932–942 | MR | Zbl

[2] V. V. Kornev, A. P. Khromov, “O ravnoskhodimosti razlozhenii po sobstvennym funktsiyam integralnykh operatorov s yadrami, dopuskayuschimi razryvy proizvodnykh na diagonalyakh”, Matem. sb., 192:10 (2001), 33–50 | MR | Zbl

[3] V. V. Kornev, A. P. Khromov, “Absolyutnaya skhodimost razlozhenii po sobstvennym i prisoedinennym funktsiyam integralnogo operatora s peremennym predelom integrirovaniya”, Izv. RAN. Ser. matem., 69:4 (2005), 59–74 | MR | Zbl

[4] N. K. Bari, Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR | Zbl