Width of shape resonances for non globally analytic potentials

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概要

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• We consider the semiclassical Schrödinger operator with a well in an island potential, on which we assume smoothness only, except near infinity. We give the asymptotic expansion of the imaginary part of the shape resonance at the bottom of the well. This is a generalization of the result by Helffer and Sjöstrand [HeSj1] in the globally analytic case. We use an almost-analytic extension in order to continue the WKB solution coming from the well beyond the caustic set, and, for the justification of the accuracy of this approximation, we develop some refined microlocal arguments in h-dependent small regions.

• 社団法人 日本数学会の論文
• 2011-01-01

著者

• Fujiie Setsuro

  Ritsumeikan University, Department of Mathematical Sciences

• Martinez Andre

  Università di Bologna, Dipartimento di Matematica

• Lahmar-benbernou Amina

  Universite De Mostaganem Department De Mathematiques

• Martinez Andre

  Universita Di Bologna Dipartimento Di Matematica

• Fujiie Setsuro

  Ritsumeikan University Department Of Mathematical Sciences

• FUJIIE SETSURO

  Ritsumeikan University

関連論文

• Width of shape resonances for non globally analytic potentials
• Width of shape resonances for non globally analytic potentials
• Semiclassical complex interactions at a non-analytic turning point (Exact WKB Analysis and Microlocal Analysis)
• Width of resonances created by homoclinic orbits : isotropic fixed point case (Spectral and Scattering Theory and Related Topics)

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