Propagation of polyhomogeneity, diffraction, and scattering on product cones
Propagation of polyhomogeneity, diffraction, and scattering on product cones
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产品锥体上多均匀性、衍射和散射的传播
DOI：
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发表时间：
2020
影响因子：
1
通讯作者：
Mengxuan Yang
中科院分区：
文献类型：
--
作者：
Mengxuan Yang
我们考虑波在乘积锥上的衍射。本文首先证明了衍射波具有一步多齐性渐近展开，改进了Cheeger-Taylor在[CT 82 a]，[CT 82 b]中关于衍射波半步多齐性的经典结果。我们还得出结论，在产品锥，散射矩阵是衍射系数，这是衍射半波核的主要标志，严格衍射相关的点的横截面上。这推广了福特，Hassell和Hillairet在二维平锥背景下的结果[FHH 18].在最后一节中，我们还给出了散射矩阵和衍射系数之间关系的辐射场解释。
We consider diffraction of waves on a product cone. We first show that diffractive waves enjoy a one-step polyhomogeneous asymptotic expansion, which is an improvement of Cheeger-Taylor's classical result of half-step polyhomogeneity of diffractive waves in [CT82a], [CT82b]. We also conclude that on product cones, the scattering matrix is the diffraction coefficient, which is the principal symbol of the diffractive half wave kernel, for strictly diffractively related points on the cross section. This generalize the result of Ford, Hassell and Hillairet in 2-dimensional flat cone settings [FHH18]. In the last section, we also give a radiation field interpretation of the relationship between the scattering matrix and the diffraction coefficient.
产品锥体上的辐射场
影响因子：
1.7
作者：
Baskin, Dean;Marzuola, Jeremy L.
通讯作者：
Marzuola, Jeremy L.
截锥体上的散射共振
DOI：
10.2140/paa.2020.2.385
发表时间：
2020
期刊：
Pure and Applied Analysis
影响因子：
--
作者：
Baskin, Dean;Yang, Mengxuan
通讯作者：
Yang, Mengxuan