PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 59(73), pp. 4976 (1996) 

Estimates for derivatives and integrals of eigenfunctions and associated functions of nonselfadjoint SturmLiouville operator with discontinuous coefficients (I)Nebojv{s}a L. Lazeti\'cMatematicki fakultet, Beograd, YugoslaviaAbstract: We consider derivatives of the eigenfunctions and associated functions of the formal SturmLiouville operator $$ \Cal L(u)(x)=\bigl(p(x)u'(x)\bigr)'+q(x)u(x) $$ defined on a finite or infinite interval $G\subseteq\Bbb R$. We suppose that the complexvalued potential $q=q(x)$ belongs to the class $L_1^{\text{\rm loc}}(G)$ and that piecewise continuously differentiable coefficient $p=p(x)$ has a finite number of the discontinuity points in $G$. Ordersharp upper estimates are obtained for the suprema of the moduli of the first derivative of the eigenfunctions and associated functions of the operator $\Cal L$ in terms of their norms in metric $L_2$ on compact subsetes of $G$ (on the entire interval $G$). Keywords: formal differential operator, eigenfunction, associated function Classification (MSC2000): 34B25 Full text of the article:
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