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Hans Christianson 《Journal of Functional Analysis》2007,246(2):145-195
For a large class of semiclassical pseudodifferential operators, including Schrödinger operators, P(h)=−h2Δg+V(x), on compact Riemannian manifolds, we give logarithmic lower bounds on the mass of eigenfunctions outside neighbourhoods of generic closed hyperbolic orbits. More precisely we show that if A is a pseudodifferential operator which is microlocally equal to the identity near the hyperbolic orbit and microlocally zero away from the orbit, then
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Hans Christianson 《偏微分方程通讯》2015,40(4):629-651
We consider quasimodes on planar domains with a partially rectangular boundary. We prove that for any ε0 > 0, an 𝒪(λ?ε0 ) quasimode must have L 2 mass in the “wings” (in phase space) bounded below by λ?2?δ for any δ > 0. The proof uses the author's recent work on 0-Gevrey smooth domains to approximate quasimodes on C 1, 1 domains. There is an improvement for C k, α and C ∞ domains. 相似文献
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