PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 60(74), pp. 3144 (1996) 

Estimates for derivatives and integrals of eigenfunctions and associated functions of nonselfadjoint SturmLiouville operator with discontinuous coefficients (II)Nebij\v sa La\v zeti\'cMatemati\v cki fakultet, Beograd, YugoslaviaAbstract: We study integrals of the eigenfunctions and associated functions of the formal SturmLiouville operator $\Cal L(u)(x)=\bigl(p(x)\,u^{\prime}(x)\bigr)^{\prime}+q(x)\,u(x)$ defined on a finite interval $G\subset\Bbb R$. We suppose that the complexvalued potential $q=q(x)$ belongs to the class $L_1(G)$ and that piecewise continuously differentiable coefficient $p=p(x)$ has a finite number of the discontinuity points in $G$. Ordersharp upper estimates are established for integrals (over arbitrary closed intervals $[y_1,y_2]\subseteq\overline G$) of the eigenfunctions and associated functions in terms of their $L_2$norms when $G$ is finite. Keywords: formal differential operator, eigenfunction, associated function Classification (MSC2000): 34B25 Full text of the article:
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