Abstract:
In this work it is proposed to study differential operators on a graph as an operator composed
of differential operators on one-dimensional arcs and matrix operators on interior vertices of the
graph. The work explores some questions concerning the theoretical side of ordinary differential
equations with integro-differential conditions on stratified sets like graph. The attention will be
paid to reconstruction of the domain of differential operator on directed graph. The reconstruction
of the domain of differential operator means a simple specifying the boundary conditions from
a known differential equations and its known eigenvalues. The paper studies the case of the
second order differential equations with irregular boundary conditions on the vertices of directed
graph. To achieve our goal we use the fact that finite set of eigenvalues serves as additional
information for reconstruction of the domain of the differential operator on stratified set. The
constructive algorithms for reconstructing the domain of definition of differential operator on
directed graph are developed. All boundary functions from the spectral data are uniquely restored.
