Recovering singular differential operators on noncompact star-type graphs from Weyl functions

Abstract

Abstract. Bessel-type differential operators on noncompact star-type graphs are studied. We establish properties of the spectral characteristics and then we investigate the inverse problem of recovering the operator from the so-called Weyl vector. For this inverse problem we prove a uniqueness theorem and propose a procedure for constructing the solution using the method of spectral mappings.

Inverse scattering problem for Sturm–Liouville operators with Bessel singularities on noncompact star-type graphs

“…Transport, spectral and scattering problems for differential operators on graphs appear frequently in mathematics, natural sciences and engineering [1][2][3][4][5][6] and are in the focus of intensive investigations [7][8][9][10][11][12][13][14][15][16][17].…”