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Resonances for Slowly Varying Perturbations of a Periodic Schrödinger Operator
Published online by Cambridge University Press: 20 November 2018
Abstract
We study the resonances of the operator $P(h)\,=\,-{{\Delta }_{x}}\,+\,V(x)\,+\,\varphi (hx)$. Here $V$ is a periodic potential, $\varphi $ a decreasing perturbation and $h$ a small positive constant. We prove the existence of shape resonances near the edges of the spectral bands of ${{P}_{0\,}}=\,-{{\Delta }_{x}}\,+\,V(x)$, and we give its asymptotic expansions in powers of ${{h}^{\frac{1}{2}}}$.
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- Copyright © Canadian Mathematical Society 2002
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