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We give pole free strips and estimates for resolvents of semiclassical operators which, on the level of the classical flow, have normally hyperbolic smooth trapped sets of codimension two in phase space.
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J. Sjöstrand and M. Zworski, Fractal upper bounds on the density of semiclassical, Duke Math. J., P 137
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J. Sjöstrand and M. Zworski, Fractal upper bounds on the density of semiclassical resonances, Duke Math. J., P 137
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J. Sjöstrand and M. Zworski, Quantum monodromy and semiclassical trace formulae, J. Math. Pure Appl. 81
2002
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N. Burq, Smoothing effect for Schrödinger boundary value problems,
2004
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N. Burq and M. Zworski, Control in the presence of a black box,
2004
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M. Zworski, Fractal Weyl laws for quantum resonances , Talk at Ecole Polytechnique, Novembre 2004, http://math.berkeley.edu/ zworski/talkX.ps
2004
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P. Stefanov, Approximating resonances with the complex absorbing potential method. Comm. Partial Differential Equations, 30(10-12):1843–1862, 2005
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P. Blue and J. Sterbenz, Uniform decay of local energy and the semi-linear wave equation on Schwarzschild space, Comm. Math. Phys. 268
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2008
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K. Datchev, Local smoothing for scattering manifolds with hyperbolic trapped sets,
2009
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S. Nonnenmacher and M. Zworski, Quantum decay rates in chaotic scattering, Acta Mathematica 203
2009
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S. Nonnenmacher and M. Zworski, Semiclassical resolvent estimates in chaotic scattering , Applied Mathematics Research eXpress 2009; doi: 10.1093/amrx/abp003
2009
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N. Burq, C. Guillarmou, and A. Hassell, Strichartz estimates without loss on manifolds with hyperbolic trapped geodesics,
2010
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V. Petkov and L. Stoyanov, Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function,
2010
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M. Zworski, Resonances in Physics and Geometry,
2011
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Jared Wunsch and Maciej Zworski, Resolvent estimates for normally hyperbolic trapped sets, Ann. Henri Poincaré, 12(7):1349–1385, 2011
2011
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M. Zworski, Semiclassical Analysis, Graduate Studies in Mathematics 138
2012
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