On complex perturbations of infinite band Schrödinger operators
DOI:
Keywords:
Schrödinger operators, infinite-band spectrum, Lieb-Thirring type inequalities, relatively compactperturbations, resolvent identityAbstract
Let $H_0=-\frac{d^2}{dx^2}+V_0$ be an infinite band Schrödinger operator on $L^2(\mathbb R)$ with a real-valued potential $V_0\in L^\infty(\mathbb R)$. We study its complex perturbation $H=H_0+V$, defined in the form sense, and obtain the Lieb-Thirring type inequ\-alities for the rate of convergence of the discrete spectrum of $H$ to the joint essential spectrum. The assumptions on $V$ vary depending on the sign of $Re V$.References
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