Harmonic manifolds of hypergeometric type and spherical Fourier transform
| Autor: | Hiroyasu Satoh, Mitsuhiro Itoh |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Gauss Mathematics::Classical Analysis and ODEs Hadamard manifold Harmonic (mathematics) 53C21 43A90 42B10 Hypergeometric distribution Convolution Volume entropy Plancherel theorem Computational Theory and Mathematics Differential Geometry (math.DG) FOS: Mathematics Geometry and Topology Hypergeometric function Analysis Mathematics |
| DOI: | 10.48550/arxiv.2005.13115 |
| Popis: | 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. Comment: 29 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|