Geodesic
On the Completeness of the System of Root Vectors of the Sturm--Liouville Operator with General Boundary Conditions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 3, pp. 45-52.

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We study general boundary value problems with nondegenerate characteristic determinant $\Delta(\lambda)$ for the Sturm–Liouville equation on the interval $[0,1]$. Necessary and sufficient conditions for the completeness of root vectors are obtained in terms of the potential. In particular, it is shown that if $\Delta(\lambda)\ne\mathrm{const}$, $q(\cdot)\in C^k[0,1]$ for some $k\ge 0$, and $q^{(k)}(0)\ne(-1)^kq^{(k)}(1)$, then the system of root vectors is complete and minimal in $L^p[0,1]$ for $p\in[1,\infty)$.
Mots-clés : Sturm–Liouville equation
Keywords: completeness of the system of root vectors, nondegenerate boundary conditions. 
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M. M. Malamud. On the Completeness of the System of Root Vectors of the Sturm--Liouville Operator with General Boundary Conditions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 3, pp. 45-52. http://geodesic.mathdoc.fr/item/FAA_2008_42_3_a3/

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