TY - JOUR

T1 - Moment conditions and support theorems for Radon transforms on affine Grassmann manifolds

AU - Gonzalez, Fulton B.

AU - Kakehi, Tomoyuki

N1 - Copyright:
Copyright 2006 Elsevier B.V., All rights reserved.

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

VL - 201

SP - 516

EP - 548

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -