TY - JOUR
T1 - Moment conditions and support theorems for Radon transforms on affine Grassmann manifolds
AU - Gonzalez, Fulton B.
AU - Kakehi, Tomoyuki
PY - 2006/4/1
Y1 - 2006/4/1
N2 - Let G(p, n) and G(q, n) be the affine Grassmann manifolds of p- and q-planes in ℝn, respectively, and let 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 ℛ(p,q) via moment conditions. We then use this range result to prove a support theorem for ℛ(p,q). This complements a previous range characterization theorem for 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.
AB - Let G(p, n) and G(q, n) be the affine Grassmann manifolds of p- and q-planes in ℝn, respectively, and let 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 ℛ(p,q) via moment conditions. We then use this range result to prove a support theorem for ℛ(p,q). This complements a previous range characterization theorem for 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.
KW - Grassmannian
KW - Moment condition
KW - Radon transform
KW - Support theorem
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U2 - 10.1016/j.aim.2005.02.009
DO - 10.1016/j.aim.2005.02.009
M3 - Article
AN - SCOPUS:33644849473
SN - 0001-8708
VL - 201
SP - 516
EP - 548
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 2
ER -