Geodesic
Estimates for Derivatives and Integrals of Eigenfunctions and Associated Functions of Nonselfadjoint Sturm-Lliouville Operator With Discontinuous Coefficients (I)
Publications de l'Institut Mathématique, _N_S_59 (1996) no. 73, p. 49

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We consider derivatives of the eigenfunctions and associated functions of the formal Sturm--Liouville 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 complex-valued 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 $G$.Order-sharp 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 $G$).
Classification : 34B25
Keywords: formal differential operator, eigenfunction, associated function 
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     author = {Neboj\v{s}a L. La\v{z}eti\'c},
     title = {Estimates for {Derivatives} and {Integrals} of {Eigenfunctions} and {Associated} {Functions} of {Nonselfadjoint} {Sturm-Lliouville} {Operator} {With} {Discontinuous} {Coefficients} {(I)}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {49 },
     publisher = {mathdoc},
     volume = {_N_S_59},
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     year = {1996},
     language = {en},
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Nebojša L. Lažetić. Estimates for Derivatives and Integrals of Eigenfunctions and Associated Functions of Nonselfadjoint Sturm-Lliouville Operator With Discontinuous Coefficients (I). Publications de l'Institut Mathématique, _N_S_59 (1996) no. 73, p. 49 . http://geodesic.mathdoc.fr/item/PIM_1996_N_S_59_73_a5/