On the relationship between the multiplicities of eigenvalues in finite- and infinite-dimensional problems on graphs

Abstract

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 normal eigenvalues (bound states) of the Sturm – Liouville operator on a star graph.