超几何型调和流形与球面傅里叶变换
Harmonic manifolds of hypergeometric type and spherical Fourier transform
摘要：
研究了具有正体积熵的调和Hadamard流形$(X^n, g)$上的球面傅里叶变换.如果$(X^n, g)$是超几何型的，即$X$的球函数用高斯超几何函数表示，则反演公式、卷积法则和Plancherel定理都由球函数用高斯超几何函数表示来表示.利用测地球的体积密度导出了超几何型的几何刻画。讨论了$(X^n, g)$的几何性质。
英文摘要：
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.
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