This article is cited in 12 papers

Completeness of eigenfunctions of one class of pencils of differential operators with constant coefficients

V. S. Rykhlov

Chair of Differential Equations and Applied Mathematics, Saratov State University, Saratov, Russia

Abstract: In this paper, in spaces of functions square summable on finite intervals we study the one-fold completeness of the system of eigen- and associated functions for the pencil of ordinary differential operators generated by a differential expression with constant coefficients (we assume that the roots of the corresponding characteristic equation lie on one and the same ray) and specific semisplitting homogeneous boundary value conditions.

Keywords: multiple completeness, one-fold completeness, eigen- and associated functions, pencil of ordinary differential operators.

UDC: 517.927.25

Received: 02.04.2007

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:6, 33–43

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