Recovering Variable Order Differential Operators with Regular Singularities on Graphs

Abstract

We study inverse spectral problems for ordinary differential equations with regular singularities on compact star-type graphs when differential equations have different orders on diferent edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.

10 pages. arXiv admin note: substantial text overlap with arXiv:1410.2007; text overlap with arXiv:1309.5360 by other authors