Geodesic
On a~representation of the kernels of resolvents of Volterra operators and its applications
Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 209-227

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

By using an integral representation for the kernel $M(x,t,\lambda)$ of the operator $(E-\nobreak\lambda^n M)^{-1}M$, where $E$ is the identity operator, and $Mf(x)=\int_0^xM(x,t)f(t)\,dt$, formulas are obtained for transformation operators of the solutions of integro-differential equations which generalize results of Ju. N. Valitskii (RZhMat., 1966, 4Б285); results of L. A. Sahnovich (RZhMat., 1960, 5409) on the linear equivalence of Volterra operators are generalized; and the question of the expansion in eigenfunctions of one-dimensional perturbations of Volterra operators is studied. Bibliography: 11 titles. 
@article{SM_1972_18_2_a3,
     author = {A. P. Khromov},
     title = {On a~representation of the kernels of resolvents of {Volterra} operators and its applications},
     journal = {Sbornik. Mathematics},
     pages = {209--227},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_18_2_a3/}
}
TY  - JOUR
AU  - A. P. Khromov
TI  - On a~representation of the kernels of resolvents of Volterra operators and its applications
JO  - Sbornik. Mathematics
PY  - 1972
SP  - 209
EP  - 227
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1972_18_2_a3/
LA  - en
ID  - SM_1972_18_2_a3
ER  - 
%0 Journal Article
%A A. P. Khromov
%T On a~representation of the kernels of resolvents of Volterra operators and its applications
%J Sbornik. Mathematics
%D 1972
%P 209-227
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1972_18_2_a3/
%G en
%F SM_1972_18_2_a3
A. P. Khromov. On a~representation of the kernels of resolvents of Volterra operators and its applications. Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 209-227. http://geodesic.mathdoc.fr/item/SM_1972_18_2_a3/