Geodesic
Eigenfunctions of the Sturm-Liouville problem on a~star graph
Sbornik. Mathematics, Tome 199 (2008) no. 10, pp. 1523-1545

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The paper considers the Sturm-Liouville problem on a star graph and is concerned with the structure and properties of the eigenvalues and eigenfunctions of this problem. Particular emphasis has been placed on the completeness of the system of eigenfunctions in the space of square-integrable functions and on the expansion of a given function as a generalized Fourier series in terms of this system. Such problems have great value in the study of boundary-value problems for linear partial differential equations on a graph by the Fourier method, and arise, for example, in the model of oscillatory processes in an elastic mast with supporting elastic guys. Bibiliography: 8 titles. 
@article{SM_2008_199_10_a5,
     author = {V. V. Provotorov},
     title = {Eigenfunctions of the {Sturm-Liouville} problem on a~star graph},
     journal = {Sbornik. Mathematics},
     pages = {1523--1545},
     publisher = {mathdoc},
     volume = {199},
     number = {10},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2008_199_10_a5/}
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V. V. Provotorov. Eigenfunctions of the Sturm-Liouville problem on a~star graph. Sbornik. Mathematics, Tome 199 (2008) no. 10, pp. 1523-1545. http://geodesic.mathdoc.fr/item/SM_2008_199_10_a5/