Geodesic
On recovering integro-differential operators from the Weyl function
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 17 (2017) no. 3, pp. 276-284

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

We study inverse problems of spectral analysis for second order integro-differential operators, which are a perturbation of the Sturm–Liouville operator by the integral Volterra operator. We pay the main attention to the nonlinear inverse problem of recovering the potential from the given Weyl function provided that the kernel of the integral operator is known a priori. We obtain properties of the spectral characteristics and the Weyl function, provide an algorithm for constructing the solution of the inverse problem and establish the uniqueness of the solution. For solving the inverse problem we use the method of standard models. 
@article{ISU_2017_17_3_a3,
     author = {M. Yu. Ignatiev and S. Yu. Sovetnikova},
     title = {On recovering integro-differential operators from the {Weyl} function},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {276--284},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2017_17_3_a3/}
}
TY  - JOUR
AU  - M. Yu. Ignatiev
AU  - S. Yu. Sovetnikova
TI  - On recovering integro-differential operators from the Weyl function
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2017
SP  - 276
EP  - 284
VL  - 17
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2017_17_3_a3/
LA  - ru
ID  - ISU_2017_17_3_a3
ER  - 
%0 Journal Article
%A M. Yu. Ignatiev
%A S. Yu. Sovetnikova
%T On recovering integro-differential operators from the Weyl function
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2017
%P 276-284
%V 17
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2017_17_3_a3/
%G ru
%F ISU_2017_17_3_a3
M. Yu. Ignatiev; S. Yu. Sovetnikova. On recovering integro-differential operators from the Weyl function. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 17 (2017) no. 3, pp. 276-284. http://geodesic.mathdoc.fr/item/ISU_2017_17_3_a3/