Geodesic
Equiconvergence of expansions in eigenfunctions of integral operators with kernels that can have discontinuities on the diagonals
Sbornik. Mathematics, Tome 192 (2001) no. 10, pp. 1451-1469 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Simple conditions are found ensuring the equiconvergence of the Fourier expansion of a function $f(x)$ in $L[0,1]$ in the eigenfunctions and the associated functions of an integral operator $$ Af=\int_0^{1-x}A(1-x,t)f(t)\,dt+\alpha\int_0^xA(x,t)f(t)\,dt $$ and the expansions of $f(x)$ and $f(1-x)$ in the standard trigonometric system. 
@article{SM_2001_192_10_a2,
     author = {V. V. Kornev and A. P. Khromov},
     title = {Equiconvergence of expansions in eigenfunctions of integral operators with kernels that can have discontinuities on the~diagonals},
     journal = {Sbornik. Mathematics},
     pages = {1451--1469},
     year = {2001},
     volume = {192},
     number = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_10_a2/}
}
TY  - JOUR
AU  - V. V. Kornev
AU  - A. P. Khromov
TI  - Equiconvergence of expansions in eigenfunctions of integral operators with kernels that can have discontinuities on the diagonals
JO  - Sbornik. Mathematics
PY  - 2001
SP  - 1451
EP  - 1469
VL  - 192
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/SM_2001_192_10_a2/
LA  - en
ID  - SM_2001_192_10_a2
ER  - 
%0 Journal Article
%A V. V. Kornev
%A A. P. Khromov
%T Equiconvergence of expansions in eigenfunctions of integral operators with kernels that can have discontinuities on the diagonals
%J Sbornik. Mathematics
%D 2001
%P 1451-1469
%V 192
%N 10
%U http://geodesic.mathdoc.fr/item/SM_2001_192_10_a2/
%G en
%F SM_2001_192_10_a2
V. V. Kornev; A. P. Khromov. Equiconvergence of expansions in eigenfunctions of integral operators with kernels that can have discontinuities on the diagonals. Sbornik. Mathematics, Tome 192 (2001) no. 10, pp. 1451-1469. http://geodesic.mathdoc.fr/item/SM_2001_192_10_a2/

[1] Khromov A. P., “Teoremy ravnoskhodimosti dlya integro-differentsialnykh i integralnykh operatorov”, Matem. sb., 114 (156):3 (1981), 378–405 | MR | Zbl

[2] Khromov A. P., “Teorema ravnoskhodimosti dlya integralnogo operatora s peremennym verkhnim predelom integrirovaniya”, Metricheskaya teoriya funktsii i smezhnye voprosy analiza, Sbornik statei, posvyaschennyi 70-letiyu P. L. Ulyanova, Izd-vo AFTs, M., 1999, 255–266 | MR

[3] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969 | MR

[4] Bellman R., Kuk K., Differentsialno-raznostnye uravneniya, Mir, M., 1967 | MR | Zbl