The λ-Cosine Transforms, Differential Operators, and Funk Transforms on Stiefel and Grassmann Manifolds

2020/07/07 by Boris Rubin, Rubin, Boris
Computer Science · Mathematics · Physics and Astronomy · #44A12 #Advanced Differential Geometry Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2007.03790

openalex publication_date 2020/07/07 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We introduce a new family of invariant differential operators associated with λ-cosine and Funk-Radon transforms on Stiefel and Grassmann manifolds. These operators reduce the order of the λ-cosine transforms and yield new inversion formulas. Intermediate Funk-cosine transforms corresponding to integration over matrices of lower rank are studied. The main tools are polar decomposition and Fourier analysis on matrix space.

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