球面上的卷积：与微分算子的交换
Convolutions on the Sphere: Commutation with Differential Operators
摘要：
推广了二维球面上向量张量卷积的定义，并证明了它与微分算子可交换。此外，与球面正交/相切的向量和张量在卷积之后仍然如此。这些性质使得新的滤波操作对于分析和建模球形系统中的非线性动力学特别有用，例如在微物理学、天体物理学和惯性约束聚变应用中。我们使用的一个重要工具是标量，矢量和张量球谐函数理论。然后，我们表明，我们的广义滤波操作是等价的（传统的）卷积的标量场的亥姆霍兹分解的矢量和张量。
英文摘要：
We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the convolution. These properties make the new filtering operation particularly useful to analyzing and modeling nonlinear dynamics in spherical systems, such as in geophysics, astrophysics, and in inertial confinement fusion applications. An essential tool we use is the theory of scalar, vector, and tensor spherical harmonics. We then show that our generalized filtering operation is equivalent to the (traditional) convolution of scalar fields of the Helmholtz decomposition of vectors and tensors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
