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Two-fold completeness of root vectors of a system of quadratic pencils

✍ Scribed by Yakov Yakubov

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 222 KB
Volume: 84
Category: Article
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2005.05.002

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✦ Synopsis

We consider a spectral problem for a system of second order (in the spectral parameter) abstract pencils in a Hilbert space and prove the completeness and the Abel basis property of a system of eigenvectors and associated vectors. In some special cases, we obtain the expansion of vectors with respect to eigenvectors. Further, it is considered a relevant application of these abstract results to boundary-value problems for second and fourth order ordinary differential equations with a quadratic spectral parameter both in the equation and in boundary-value conditions.

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## Abstract The present paper is the first one in a series of two papers devoted to a unified approach to the problem of completeness of the generalized eigenvectors (the root vectors) for a specific class of linear non‐selfadjoint unbounded differential operators. The list of the problems for whic