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. 
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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