Moment Conditions and Support Theorems for Radon Transforms on Affine Grassmann Manifolds
| dc.creator | Gonzalez, Fulton B. | |
| dc.creator | Kakehi, Tomoyuki | |
| dc.date | 2004-04-02 | |
| dc.date.accessioned | 2026-07-07T05:07:01Z | |
| dc.date.available | 2026-07-07T05:07:01Z | |
| dc.description | Let $G(p,n)$ and $G(q,n)$ be the affine Grassmann manifolds of $p$- and $q$- planes in ${\mathbb R}^n$, respectively, and let $\mathcal{R}^{(p,q)}$ be the Radon transform from smooth functions on $G(p,n)$ to smooth functions on $G(q,n)$ arising from the inclusion incidence relation. When $p<q$ and $\dim G(p,n) = \dim G(p,n)$, we present a range characterization theorem for $\mathcal{R}^{(p,q)}$ via moment conditions. We then use this range result to prove a support theorem for $\mathcal{R}^{(p,q)}$. This complements a previous range characterization theorem for $\mathcal{R}^{(p,q)}$ via differential equations when $\dim G(p,n) < \dim G(p,n)$. We also present a support theorem in this latter case. | |
| dc.identifier | https://arxiv.org/abs/math/0404036 | |
| dc.identifier | http://arxiv.org/abs/math/0404036 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70694 | |
| dc.subject | Functional Analysis | |
| dc.subject | 44A12; 43A85 | |
| dc.title | Moment Conditions and Support Theorems for Radon Transforms on Affine Grassmann Manifolds | |
| dc.type | text |