论文标题
多生物学性，衍射和散射产品锥体的传播
Propagation of polyhomogeneity, Diffraction and Scattering on Product Cones
论文作者
论文摘要
我们考虑在产品锥上波的衍射。我们首先表明衍射波具有一步的多性渐近线膨胀，这是Cheeger-Taylor在[CT82A]中衍射波的半步多态性的经典结果的改善，[CT82A]，[CT82B]。我们还得出结论，在产品锥上，散射矩阵是衍射系数，它是衍射半波核的主要符号，对于横截面上的严格衍射相关点。这概括了二维平锥设置中福特，Hassell和Hillairet的结果[FHH18]。在最后一节中，我们还提供了散射矩阵与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.
