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This article is cited in 5 scientific papers (total in 5 papers)
Mathematics
On multiple completeness of the root functions for a class of the pencils of differential operators
V. S. Rykhlov Saratov State University, Chair of Differential Equations and Applied Mathematics
Abstract:
A polinomial pencil of ordinary differential operators of $n$-th order generated by a homogeneous differential expression with constant coefficients and by two-point boundary conditions of a special structure with $l$
conditions in zero only ($1\le l\le n-1$) is considered in the space $L_2[0,1]$. The case is studied, when the roots of the characteristic equation lie on a ray coming fromthe origin. A sufficient condition of $m$-fold completeness of the system of root functions for $m\le n-l$ in the space $L_2[0,1]$ is found. An accuracy of obtained result is shown.
Key words:
pencil of ordinary differential operators, two-point boundary conditions, homogeneous differential expression with constant coefficients, multiple completeness of system of root functions, multiple completeness of system of eigen- and associated functions.
Citation:
V. S. Rykhlov, “On multiple completeness of the root functions for a class of the pencils of differential operators”, Izv. Saratov Univ. Math. Mech. Inform., 10:2 (2010), 24–34
Linking options:
https://www.mathnet.ru/eng/isu18 https://www.mathnet.ru/eng/isu/v10/i2/p24
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