Admissible Complexes for the Projective X-ray Transform over a Finite Field

被引：0

作者：

Feldman, David, V ^{[1
]}

Grinberg, Eric L. ^{[2
]}

机构：

[1] Univ New Hampshire, Dept Math, Kingsbury Hall, Durham, NH 03824 USA

[2] Univ Massachusetts, Dept Math, 100 Morrissey Blvd, Boston, MA 02125 USA

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2020年 / 64卷 / 01期

关键词：

Radon transform; X-ray transform; Integral geometry; Admissibility; Line complexes; Projective spaces; Finite fields; Doubly ruled quadric surfaces;

D O I：

10.1007/s00454-020-00207-x

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider the X-ray transform in a projective space over a finite field. It is well known (after Bolker) that this transform is injective. We formulate an analog of Gelfand's admissibility problem for the Radon transform, which asks for a classification of all minimal sets of lines for which the restricted Radon transform is injective. The solution involves doubly ruled quadric surfaces.

引用

页码：28 / 36

页数：9

共 8 条

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[4] Gelfand IM., 1966, Integral Geometry and Representation Theory: Generalized functions
[5] THE ADMISSIBILITY THEOREM FOR THE HYPERPLANE TRANSFORM OVER A FINITE-FIELD
GRINBERG, E
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 1990, 53 (02) : 316 - 320
[6] Grinberg E.L., 2012, MATH LEGACY LEON EHR, V16, P111, DOI [10.1007/978-88-470-1947-8_8, DOI 10.1007/978-88-470-1947-8_8]
[7] KIRILLOV AA, 1961, DOKL AKAD NAUK SSSR+, V137, P276
[8] Kung J.P., 1990, CONT MATH, V113, P1

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