New inversion formulas for Radon transforms on affine Grassmannians

Boris Rubin; Yingzhan Wang

doi:10.1016/j.jfa.2018.03.002

New inversion formulas for Radon transforms on affine Grassmannians

Boris Rubin
, Yingzhan Wang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We obtain new inversion formulas for the Radon transform and the corresponding dual transform acting on affine Grassmann manifolds of planes in Rⁿ. The consideration is performed in full generality on continuous functions and functions belonging to L^p spaces.

Original language	English
Pages (from-to)	2792-2817
Number of pages	26
Journal	Journal of Functional Analysis
Volume	274
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2018.03.002
State	Published - 15 May 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

Erdélyi–Kober operators
Funk transform
Grassmann manifolds
Radon transforms

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10.1016/j.jfa.2018.03.002

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title = "New inversion formulas for Radon transforms on affine Grassmannians",

abstract = "We obtain new inversion formulas for the Radon transform and the corresponding dual transform acting on affine Grassmann manifolds of planes in Rn. The consideration is performed in full generality on continuous functions and functions belonging to Lp spaces.",

keywords = "Erd{\'e}lyi–Kober operators, Funk transform, Grassmann manifolds, Radon transforms",

author = "Boris Rubin and Yingzhan Wang",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

month = may,

day = "15",

doi = "10.1016/j.jfa.2018.03.002",

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T1 - New inversion formulas for Radon transforms on affine Grassmannians

AU - Rubin, Boris

AU - Wang, Yingzhan

PY - 2018/5/15

Y1 - 2018/5/15

N2 - We obtain new inversion formulas for the Radon transform and the corresponding dual transform acting on affine Grassmann manifolds of planes in Rn. The consideration is performed in full generality on continuous functions and functions belonging to Lp spaces.

AB - We obtain new inversion formulas for the Radon transform and the corresponding dual transform acting on affine Grassmann manifolds of planes in Rn. The consideration is performed in full generality on continuous functions and functions belonging to Lp spaces.

KW - Erdélyi–Kober operators

KW - Funk transform

KW - Grassmann manifolds

KW - Radon transforms

UR - https://www.scopus.com/pages/publications/85043514504

U2 - 10.1016/j.jfa.2018.03.002

DO - 10.1016/j.jfa.2018.03.002

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AN - SCOPUS:85043514504

SN - 0022-1236

VL - 274

SP - 2792

EP - 2817

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 10

ER -

New inversion formulas for Radon transforms on affine Grassmannians

Abstract

Bibliographical note

Keywords

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