تقرير
Resolvent estimates on asymptotically cylindrical manifolds and on the half line
| العنوان: | Resolvent estimates on asymptotically cylindrical manifolds and on the half line |
|---|---|
| المؤلفون: | Christiansen, T. J., Datchev, K. |
| المصدر: | Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. Vol. 54, No. 4, pp. 1051-1088, 2021 |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematical Physics, Mathematics - Spectral Theory |
| الوصف: | Manifolds with infinite cylindrical ends have continuous spectrum of increasing multiplicity as energy grows, and in general embedded resonances (resonances on the real line, embedded in the continuous spectrum) and embedded eigenvalues can accumulate at infinity. However, we prove that if geodesic trapping is sufficiently mild, then the number of embedded resonances and eigenvalues is finite, and moreover the cutoff resolvent is uniformly bounded at high energies. We obtain as a corollary the existence of resonance free regions near the continuous spectrum. We also obtain improved estimates when the resolvent is cut off away from part of the trapping, and along the way we prove some resolvent estimates for repulsive potentials on the half line which may be of independent interest. Comment: This paper is a companion to the paper `Wave asymptotics for manifolds with infinite cylindrical ends' by the same authors, but each paper can be read independently of the other |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1705.08969 |
| رقم الأكسشن: | edsarx.1705.08969 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |