Geodesic
Absolute convergence of expansions in eigen- and adjoint functions of
Izvestiya. Mathematics, Tome 69 (2005) no. 4, pp. 703-717 
V. V. Kornev; A. P. Khromov. Absolute convergence of expansions in eigen- and adjoint functions of. Izvestiya. Mathematics, Tome 69 (2005) no. 4, pp. 703-717. http://geodesic.mathdoc.fr/item/IM2_2005_69_4_a2/
@article{IM2_2005_69_4_a2,
     author = {V. V. Kornev and A. P. Khromov},
     title = {Absolute convergence of expansions in~eigen- and adjoint functions of},
     journal = {Izvestiya. Mathematics},
     pages = {703--717},
     year = {2005},
     volume = {69},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2005_69_4_a2/}
}
TY  - JOUR
AU  - V. V. Kornev
AU  - A. P. Khromov
TI  - Absolute convergence of expansions in eigen- and adjoint functions of
JO  - Izvestiya. Mathematics
PY  - 2005
SP  - 703
EP  - 717
VL  - 69
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/IM2_2005_69_4_a2/
LA  - en
ID  - IM2_2005_69_4_a2
ER  - 
%0 Journal Article
%A V. V. Kornev
%A A. P. Khromov
%T Absolute convergence of expansions in eigen- and adjoint functions of
%J Izvestiya. Mathematics
%D 2005
%P 703-717
%V 69
%N 4
%U http://geodesic.mathdoc.fr/item/IM2_2005_69_4_a2/
%G en
%F IM2_2005_69_4_a2

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

We establish an analogue of Zygmund's criterion for the absolute convergence of trigonometric Fourier series for expansions in eigen- and adjoint functions of the integral operator $Af(x)=\int_0^{1-x}A(1-x,t)f(t)\,dt$.

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

[2] Kurdyumov V. P., Khromov A. P., “O bazisakh Rissa iz sobstvennykh funktsii integralnogo operatora s peremennym predelom integrirovaniya”, Dokl. RAN, 393:1 (2003), 14–17 | MR

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

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

[5] Keselman G. M., “O bezuslovnoi skhodimosti razlozhenii po sobstvennym funktsiyam nekotorykh differentsialnykh operatorov”, Izv. vuzov. Matematika, 1964, no. 2, 82–93 | MR

[6] Kachmazh S., Shteingauz G., Teoriya ortogonalnykh ryadov, Fizmatgiz, M., 1958 | MR