Spin群上的扩散小波
Diffusive wavelets on the Spin group
摘要：
本文的第一部分从Clifford分析的角度简要回顾了自旋群Spin（m）的表示论的研究结果。在第二部分中，我们感兴趣的Clifford值函数和小波的球。Spin（m）的表示和扩散小波的概念的连接自然导致了对球面上的一个修改的扩散方程的研究，该方程利用了Gamma算子。我们将得到关于修正的扩散算子的Clifford值扩散小波。由于我们能够刻画Spin（m）的所有表示，甚至能够在表示空间中获得（通过表示）所考虑的Casimir算子的所有特征向量，因此直接研究Spin（m）上的函数似乎是合适的。关于这一点，我们的目标将是制定的Laplace-Beltrami算子的本征函数的自旋（m），并给出了热核自旋（m）的本征函数的级数展开。
英文摘要：
The first part of this article is devoted to a brief review of the results about representation theory of the spin group Spin(m) from the point of view of Clifford analysis. In the second part we are interested in Clifford-valued functions and wavelets on the sphere. The connection of representations of Spin(m) and the concept of diffusive wavelets leads naturally to investigations of a modified diffusion equation on the sphere, that makes use of the Gamma operator. We will achieve to obtain Clifford-valued diffusion wavelets with respect to a modified diffusion operator. Since we are able to characterize all representations of Spin(m) and even to obtain all eigenvectors of the (by representation) regarded Casimir operator in representation spaces, it seems appropriate to look at functions on Spin(m) directly. Concerning this, our aim shall be to formulate eigenfunctions for the Laplace-Beltrami operator on Spin(m) and give the series expansion of the heat kernel on Spin(m) in terms of eigenfunctions.
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。
