Radon-john transforms and spherical harmonics

Ricardo Estrada; Boris Rubin

doi:10.1090/conm/714/14329

Radon-john transforms and spherical harmonics

Ricardo Estrada
, Boris Rubin

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

4 Scopus citations

Abstract

The d-plane Radon-John transform takes functions on Rⁿ to functions on the set of all d-dimensional planes in Rⁿ by integration over these planes. We study the action of this transform on degenerate functions of the form f (x) = f₀ (r) Y_k (θ), where r = |x| > 0, θ = x/|x|, and Y_k is a spherical harmonic of degree k. It is shown that the results for d < n−1 are surprisingly different from those in the known case d = n − 1.

Original language	English
Title of host publication	Contemporary Mathematics
Publisher	American Mathematical Society
Pages	131-142
Number of pages	12
DOIs	https://doi.org/10.1090/conm/714/14329
State	Published - 2018
Externally published	Yes

Publication series

Name	Contemporary Mathematics
Volume	714
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Bibliographical note

Publisher Copyright:
©2018 Amerian Mathematial Soiety.

Keywords

Gegenbauer-chebyshev integrals
Grass-mann manifolds
Radon-john transforms

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10.1090/conm/714/14329

Cite this

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abstract = "The d-plane Radon-John transform takes functions on Rn to functions on the set of all d-dimensional planes in Rn by integration over these planes. We study the action of this transform on degenerate functions of the form f (x) = f0 (r) Yk (θ), where r = |x| > 0, θ = x/|x|, and Yk is a spherical harmonic of degree k. It is shown that the results for d < n−1 are surprisingly different from those in the known case d = n − 1.",

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doi = "10.1090/conm/714/14329",

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AU - Rubin, Boris

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AB - The d-plane Radon-John transform takes functions on Rn to functions on the set of all d-dimensional planes in Rn by integration over these planes. We study the action of this transform on degenerate functions of the form f (x) = f0 (r) Yk (θ), where r = |x| > 0, θ = x/|x|, and Yk is a spherical harmonic of degree k. It is shown that the results for d < n−1 are surprisingly different from those in the known case d = n − 1.

KW - Gegenbauer-chebyshev integrals

KW - Grass-mann manifolds

KW - Radon-john transforms

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ER -

Radon-john transforms and spherical harmonics

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