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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     author = {M. M. Malamud},
     title = {On the {Completeness} of the {System} of {Root} {Vectors} of the {Sturm--Liouville} {Operator} with {General} {Boundary} {Conditions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {45--52},
     publisher = {mathdoc},
     volume = {42},
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     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2008_42_3_a3/}
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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/