We study the Segal Bargmann transform on a symmetric space X of compact type, mapping L 2 (X ) into holomorphic functions on the complexification X C . We invert this transform by integrating against a ``dual'' heat kernel measure in the fibers of a natural fibration of X C over X. We prove that the
The flat horocycle transform for a symmetric space
β Scribed by Sigurdur Helgason
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 777 KB
- Volume
- 91
- Category
- Article
- ISSN
- 0001-8708
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Penrose transform is constructed relating solutions of the Dirac equation and the conformally invariant Laplacian, on an even dimensional conformally flat manifold, to cohomology with values in a certain holomorphic line bundle over the manifolds twistor space. [10] Warner, G. "Harmonic Analysis on
## Abstract Consider the Poincare unit disk model for the hyperbolic plane **H**^2^. Let Ξ be the set of all horocycles in **H**^2^ parametrized by (__ΞΈ, p__), where __e^iΞΈ^__ is the point where a horocycle __ΞΎ__ is tangent to the boundary |__z__| = 1, and __p__ is the hyperbolic distance from __ΞΎ_
In this paper we investigate L 2 boundedness properties of the Poisson transform associated to a symmetric space of real rank one and prove a related Planchereltype theorem.