Geodesic
Equiconvergence theorem for integral operator with involution
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 17 (2017) no. 3, pp. 313-330

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

In the paper, the integral operator with kernel having discontinuities of the first kind at the lines $t=x$ and $t=1-x$ is studied. The equiconvergence of Fourier expansions for arbitrary integrable function $f(x)$ in eigenfunctions and associated functions of the considered operator and expansions of linear combination of functions $f(x)$ and $f(1-x)$ in trigonometric system is proved. The equiconvergence is studied using the method based on integration of the resolvent using spectral value. Methods, developed by A. P. Khromov in the study of spectral theory of integral operators are widely used. Recently, these methods are of use in studies of boundary value problems of mathematical physics using Fourier method with minimal smoothness conditions for the initial data. 
@article{ISU_2017_17_3_a7,
     author = {E. V. Nazarova and V. A. Khalova},
     title = {Equiconvergence theorem for integral operator with involution},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {313--330},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2017_17_3_a7/}
}
TY  - JOUR
AU  - E. V. Nazarova
AU  - V. A. Khalova
TI  - Equiconvergence theorem for integral operator with involution
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2017
SP  - 313
EP  - 330
VL  - 17
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2017_17_3_a7/
LA  - ru
ID  - ISU_2017_17_3_a7
ER  - 
%0 Journal Article
%A E. V. Nazarova
%A V. A. Khalova
%T Equiconvergence theorem for integral operator with involution
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2017
%P 313-330
%V 17
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2017_17_3_a7/
%G ru
%F ISU_2017_17_3_a7
E. V. Nazarova; V. A. Khalova. Equiconvergence theorem for integral operator with involution. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 17 (2017) no. 3, pp. 313-330. http://geodesic.mathdoc.fr/item/ISU_2017_17_3_a7/