Radon inversion on Grassmannians via Garding-Gindikin fractional integrals

• 成果类型: Article
• 署名作者: Grinberg, EL; Rubin, B
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2004.159.783
• 发表日期: 2004
• 页码: 783-817
• 关键词: bessel functions; Transforms; formulas; cosine

摘要

We study the Radon transform Rf of functions on Stiefel and Grassmann manifolds. We establish a connection between Rf and G (a) over circle rding-Gindikin fractional integrals associated to the cone of positive definite matrices. By using this connection, we obtain Abel-type representations and explicit inversion formulae for Rf and the corresponding dual Radon transform. We work with the space of continuous functions and also with L-p spaces.