Conditions for the \(k\)-fold completeness (\(0 < k \leq n\)) of root functions of an \(n\)th-order ordinary differential operator pencil (Q2459688)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Conditions for the \(k\)-fold completeness (\(0 < k \leq n\)) of root functions of an \(n\)th-order ordinary differential operator pencil |
scientific article |
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Conditions for the \(k\)-fold completeness (\(0 < k \leq n\)) of root functions of an \(n\)th-order ordinary differential operator pencil (English)
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8 November 2007
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The paper deals with the linear differential operator pencil \[ \sum_{s+j\leq n} P_{sj}\lambda^s y^{(j)}(x),\quad 0<x<1, \] with constant complex coefficients \(P_{sj}\), where \(\lambda\) is a complex parameter and with suitable boundary conditions. The authors obtain simple conditions for the \(k\)-fold completeness of the system of root functions for the problem under consideration.
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\(k\)-fold completeness
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ordinary differential operator
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operator pencil
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