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Spectral completeness of the root functions of a boundary value problem on a graph. (English. Russian original) Zbl 0831.34085
Russ. Acad. Sci., Dokl., Math. 49, No. 2, 298-302 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 335, No. 3, 281-283 (1994).
The spectral boundary value problem $$(Pu')' + qu = \lambda u$$, $$u |_{\partial \Gamma} = 0$$, is considered. Here $$\Gamma$$ is a finite geometric graph. The structure of the spectrum is described and the completeness of the root functions is proved.

##### MSC:
 34L05 General spectral theory of ordinary differential operators 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B27 Green’s functions for ordinary differential equations 35K05 Heat equation 05C99 Graph theory