Geodesic
Estimates for Derivatives and Integrals of Eigenfunctions and Associated Functions of Nonselfadjoint Sturm-Liouville Operator With Discontinuous Coefficients (II)
Publications de l'Institut Mathématique, _N_S_60 (1996) no. 74, p. 31

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We study integrals of the eigenfunctions and associated functions of the formal Sturm--Liouville 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 complex-valued 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 $G$. Order-sharp 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.
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-Liouville} {Operator} {With} {Discontinuous} {Coefficients} {(II)}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {31 },
     publisher = {mathdoc},
     volume = {_N_S_60},
     number = {74},
     year = {1996},
     zbl = {0930.34062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1996_N_S_60_74_a4/}
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Nebojša L. Lažetić. Estimates for Derivatives and Integrals of Eigenfunctions and Associated Functions of Nonselfadjoint Sturm-Liouville Operator With Discontinuous Coefficients (II). Publications de l'Institut Mathématique, _N_S_60 (1996) no. 74, p. 31 . http://geodesic.mathdoc.fr/item/PIM_1996_N_S_60_74_a4/