On Multiple Completeness of the Root Functions of a Certain Class of Pencils of Differential Operators with Constant Coefficients

V. S. Rykhlov ; O. V. Blinkova

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 574-584.

Résumé

We consider the class of pencils of ordinary differential operators of $n$-th order with constant coefficients. It is assumed that the roots of the characteristic equation of pencils from this class are simple, non-zero and lie on the same straight line passing through the origin. Sufficient conditions for $n$-fold completeness of the system of root functions of the pencils from this class in the space of summable with square functions on the main segment are formulated.

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