03-173 O.A.Veliev, M.Toppamuk Duman

On the Sturm-Liouville Operator with Summable Potential (38K, LATeX 2e) Apr 14, 03

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Abstract. We investigate the Sturm-Liouville operator \[ L(q)=-\frac{d^{2}}{dx^{2}}+q(x) \] in $L_{2}[0,1]$ with strongly regular boundary conditions and arbitrary Lebesque integrable Potential $q(x)$. We obtain asymptotic formulas of arbitrary order for eigenvalues and eigenfunctions of $L(q).$ Besides we give a simple proof of Riesz basisness of eigenfunctions and associeted functions of this operator.

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