On the Relationship Between the Multiplicities of Eigenvalues in Finite- and Infinite-Dimensional Problems on Graphs

It is shown that some results concerning the multiplicities of eigenvalues of the spectral problem that describes small transverse vibrations of a star graph of Stieltjes strings and the multiplicities of the eigenvalues of tree-patterned matrices can be used for the description of possible multiplicities of the normal eigenvalues (bound states) of the Sturm–Liouville operator on a star graph.