Expansion in eigenfunctions of the Sturm--Liouville problem on a graph bundle
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2008), pp. 50-62.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider the applicability of the Fourier method for partial differential equations on spatial grids (we choose a bundle graph as a model). This leads to an important problem, namely, to the expansion of a given function in eigenfunctions of the corresponding Sturm–Liouville problem on a grid. We study a model problem which describes a symmetric case, when one considers physically identical one-dimensional continuums on the bundle graph. Such problems arise, for example, in the modeling of oscillating processes of an elastic mast with supporting elastic ties.
Keywords: boundary-value problem on a graph, eigenfunctions, the Green function, completeness of system of eigenfunctions, expansion in eigenfunctions.
@article{IVM_2008_3_a4,
     author = {V. V. Provotorov},
     title = {Expansion in eigenfunctions of the {Sturm--Liouville} problem on a graph bundle},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {50--62},
     publisher = {mathdoc},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_3_a4/}
}
TY  - JOUR
AU  - V. V. Provotorov
TI  - Expansion in eigenfunctions of the Sturm--Liouville problem on a graph bundle
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2008
SP  - 50
EP  - 62
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2008_3_a4/
LA  - ru
ID  - IVM_2008_3_a4
ER  - 
%0 Journal Article
%A V. V. Provotorov
%T Expansion in eigenfunctions of the Sturm--Liouville problem on a graph bundle
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2008
%P 50-62
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2008_3_a4/
%G ru
%F IVM_2008_3_a4
V. V. Provotorov. Expansion in eigenfunctions of the Sturm--Liouville problem on a graph bundle. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2008), pp. 50-62. http://geodesic.mathdoc.fr/item/IVM_2008_3_a4/

[1] Pokornyi Yu. V., Penkin O. M., Pryadiev V. L., Borovskikh A. V., Lazarev K. P., Shabrov S. A., Differentsialnye uravneniya na geometricheskikh grafakh, Fizmatlit, M., 2004, 227 pp. | Zbl

[2] Levitan B. M., Sargsyan I. S., Vvedenie v spektralnuyu teoriyu. Samosopryazhennye obyknovennye differentsialnye operatory, Nauka, M., 1970, 671 pp. | MR | Zbl

[3] Yurko V. A., Obratnye spektralnye zadachi i ikh prilozheniya, Izd-vo Saratovsk. ped. in-ta, Saratov, 2001, 499 pp.

[4] Shabat B. V., Vvedenie v kompleksnyi analiz. Ch. 1. Funktsii odnogo peremennogo, Nauka, M., 1976, 320 pp.