Spectral concentration in Sturm-Liouville equations with large negative potential

We consider the spectral function, $ho_{alpha} (lambda)$, associated with the linear second-order question $$ y'' + (lambda - q(x)) y = 0 quad hbox{in } [0, infty) $$ and the initial condition $$ y(0) cos (alpha) + y' (0) sin (alpha) = 0, quad alpha in [0, pi). $$ in the case where $q...

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2010; no. 133; pp. 1 - 10
Main Authors Bernard J. Harris, Jeffrey C. Kallenbach
Format Journal Article
LanguageEnglish
Published Texas State University 14.09.2010
Subjects
Schrodinger equation
Spectral theory
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Summary:We consider the spectral function, $ho_{alpha} (lambda)$, associated with the linear second-order question $$ y'' + (lambda - q(x)) y = 0 quad hbox{in } [0, infty) $$ and the initial condition $$ y(0) cos (alpha) + y' (0) sin (alpha) = 0, quad alpha in [0, pi). $$ in the case where $q (x) o - infty$ as $x o infty$. We obtain a representation of $ho_0 (lambda)$ as a convergent series for $lambda > Lambda_0$ where $Lambda_0$ is computable, and a bound for the points of spectral concentration.
ISSN:1072-6691