Harmonic analysis for spinors on real hyperbolic spaces
Harmonic analysis for spinors on real hyperbolic spaces
复制标题
实双曲空间上旋量的调和分析
DOI：
10.4064/cm87-2-10
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
E. Pedon
中科院分区：
文献类型：
--
作者：
R. Camporesi;E. Pedon
我们在实双曲空间H^n(R)上发展了(狄拉克)旋量的$L^2$调和分析，并给出了类似于函数和微分形式的经典概念和结果：我们研究了泊松变换、球函数理论、球面傅里叶变换和傅里叶变换。通过归结到$L^2(R)$上的雅可比分析，得到了非常明确的表达式和陈述。作为应用，我们描述了狄拉克算符的精确谱，研究了阿贝尔变换，并导出了与旋量拉普拉斯算符相关的热核的显式表达式
We develop the $L^2$ harmonic analysis for (Dirac) spinors on the real hyperbolic space $H^n(\R)$ and give the analogue of the classical notions and results known for functions and differential forms: we investigate the Poisson transform, the spherical function theory, the spherical Fourier transform and the Fourier transform. Very explicit expressions and statements are obtained by reduction to Jacobi analysis on $L^2(\R)$. As applications, we describe the exact spectrum of the Dirac operator, study the Abel transform and derive explicit expressions for the heat kernel associated with the spinor Laplacian