تقرير
Wave propagation on Euclidean surfaces with conical singularities. I: Geometric diffraction
| العنوان: | Wave propagation on Euclidean surfaces with conical singularities. I: Geometric diffraction |
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| المؤلفون: | Ford, G. Austin, Hassell, Andrew, Hillairet, Luc |
| سنة النشر: | 2015 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 35L05, 35S30, 58J50 |
| الوصف: | We investigate the singularities of the trace of the half-wave group, $\mathrm{Tr} \, e^{-it\sqrt\Delta}$, on Euclidean surfaces with conical singularities $(X,g)$. We compute the leading-order singularity associated to periodic orbits with successive degenerate diffractions. This result extends the previous work of the third author \cite{Hil} and the two-dimensional case of the work of the first author and Wunsch \cite{ForWun} as well as the seminal result of Duistermaat and Guillemin \cite{DuiGui} in the smooth setting. As an intermediate step, we identify the wave propagators on $X$ as singular Fourier integral operators associated to intersecting Lagrangian submanifolds, originally developed by Melrose and Uhlmann \cite{MelUhl}. Comment: 45 pages, 2 figures. Comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1505.01043 |
| رقم الأكسشن: | edsarx.1505.01043 |
| قاعدة البيانات: | arXiv |
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