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تسجيل مستخدم جديدDecay rates at infinity for solutions to periodic Schr{o}dinger equations
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تأليف
Daniel M. Elton
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We consider the equation $Delta u=Vu$ in exterior domains in $mathbb{R}^2$ and $mathbb{R}^3$, where $V$ has certain periodicity properties. In particular we show that such equations cannot have non-trivial superexponentially decaying solutions. As an application this leads to a new proof for the absolute continuity of the spectrum of particular periodic Schr{o}dinger operators. The equation $Delta u=Vu$ is studied as part of a broader class of elliptic evolution equations.
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