Dual Radon transforms on affine Grassmann manifolds期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Dual Radon transforms on affine Grassmann manifolds

Authors:	Fulton B Gonzalez Tomoyuki Kakehi

Institution:	Department of Mathematics, Tufts University, Medford, Massachusetts 02155-7049 ; Institute of Mathematics, University of Tsukuba, Ibaraki, Japan 305-8571

Abstract:	Fix $0 \leq p < q \leq n-1$ , and let and denote the affine Grassmann manifolds of - and -planes in $\mathbb{R} ^n$ . We investigate the Radon transform $\mathcal{R}^{(q,p)} : C^{\infty} (G(q,n)) \to C^{\infty} (G(p,n))$ associated with the inclusion incidence relation. For the generic case $\dim G(q,n) < \dim G(p,n)$ and , we will show that the range of this transform is given by smooth functions on annihilated by a system of Pfaffian type differential operators. We also study aspects of the exceptional case .

Keywords:	Radon transform Grassmannian Pfaffian systems

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