论文标题
高几何类型和球形傅立叶变换的谐波歧管
Harmonic manifolds of hypergeometric type and spherical Fourier transform
论文作者
论文摘要
研究了谐波的hadamard歧管$（x^n，g）$的球形傅立叶变换。如果$（x^n，g）$具有超几何类型，即$ x $的球形函数由高斯超几何函数（反转公式）表示，则卷积规则与plancherel定理一起显示由高斯球体函数的表示，以高斯高度高度函数的形式表示。超几何类型的几何表征是根据测量球的体积密度得出的。还讨论了$（x^n，g）$的几何属性。
The spherical Fourier transform on a harmonic Hadamard manifold $(X^n, g)$ of positive volume entropy is studied. If $(X^n, g)$ is of hypergeometric type, namely spherical functions of $X$ are represented by the Gauss hypergeometric functions, the inversion formula, the convolution rule together with the Plancherel theorem are shown by the representation of the spherical functions in terms of the Gauss hypergeometric functions. A geometric characterization of hypergeometric type is derived in terms of volume density of geodesic spheres. Geometric properties of $(X^n, g)$ are also discussed.
