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- W2256777216 abstract "We study resonances of compactly supported potentials $ V_varepsilon = W ( x, x/varepsilon ) $ where $ W : mathbb{R}^d times mathbb{R}^d / ( 2pi mathbb{Z}) ^d to mathbb{C} $, $ d $ odd. That means that $ V_varepsilon $ is a sum of a slowly varying potential, $ W_0 ( x) $, and one oscillating at frequency $1/varepsilon$. For $ W_0 equiv 0 $ we prove that there are no resonances above the line $text{Im} lambda = -A ln(varepsilon^{-1})$, except possibly a simple resonance of modulus $sim varepsilon^2$, when $ d=1$. We show that this result is optimal by constructing a one-dimensional example. In the case when $ W_0 neq 0 $ we prove that resonances in fixed strips admit an expansion in powers of $varepsilon$. The argument provides a method for computing the coefficients of the expansion. In particular we produce an effective potential converging uniformly to $W_0$ as $varepsilon rightarrow 0$ and whose resonances approach resonances of $V_varepsilon$ modulo $O(varepsilon^4)$." @default.
- W2256777216 created "2016-06-24" @default.
- W2256777216 creator A5008103793 @default.
- W2256777216 date "2015-09-14" @default.
- W2256777216 modified "2023-09-27" @default.
- W2256777216 title "Scattering resonances for highly oscillatory potentials" @default.
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