Wave propagation on Euclidean surfaces with conical singularities. I: Geometric diffraction
Wave propagation on Euclidean surfaces with conical singularities. I: Geometric diffraction
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具有圆锥奇点的欧几里得表面上的波传播。
DOI：
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发表时间：
2015
期刊：
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通讯作者：
L. Hillairet
中科院分区：
文献类型：
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作者：
Andrew Hassell;L. Hillairet
本文研究了半波群$mathrm{Tr}，e^{-itsqrtDelta}$在具有圆锥奇点$（X，g）$的欧氏曲面上的迹的奇性。我们计算了与连续退化衍射周期轨道相关的首阶奇异性。这一结果推广了第三作者引用{Hil}的工作和第一作者和Wunsch引用{ForWun}的工作的二维情况以及Duistermaat和Guillemin引用{DuiGui}在光滑设置中的开创性结果。作为一个中间步骤，我们确定的波传播$X$奇异傅立叶积分算子相关联的相交拉格朗日子流形，最初开发的Melrose和Uhlmann引用{MelUhl}。
We investigate the singularities of the trace of the half-wave group, $mathrm{Tr} , e^{-itsqrtDelta}$, 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}.