Fractal upper bounds on the density of semiclassical resonances
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🧮 math.SP
math.AP
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boundsresonancessemiclassicalupperalongaxisboxesdensity
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For semiclassical problems we establish upper bounds on the number of resonances in boxes of size $h$ along the real axis, in terms of the dimension of the set of trapped trajectories. The proof uses second microlocalization.
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