On the kernel of the maximal flat Radon transform on symmetric spaces of compact type

Eric L. Grinberg; Steven Glenn Jackson

On the kernel of the maximal flat Radon transform on symmetric spaces of compact type

Mathematics

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

Abstract

Let M be a Riemannian globally symmetric space of compact type, M′ its set of maximal flat totally geodesic tori, and Ad(M) its adjoint space. We show that the kernel of the maximal flat Radon transform τ : L² (M) → L² (M′ ) is precisely the orthogonal complement of the image of the pullback map L² (Ad(M)) → L² (M). In particular, we show that the maximal flat Radon transform is injective if and only if M coincides with its adjoint space.

Original language	English
Pages (from-to)	623-636
Number of pages	14
Journal	Journal of Lie Theory
Volume	27
Issue number	3
State	Published - 2017

ASJC Scopus Subject Areas

Algebra and Number Theory

Keywords

Integral geometry
Radon transform
Symmetric space

Cite this

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abstract = "Let M be a Riemannian globally symmetric space of compact type, M′ its set of maximal flat totally geodesic tori, and Ad(M) its adjoint space. We show that the kernel of the maximal flat Radon transform τ : L2 (M) → L2 (M′ ) is precisely the orthogonal complement of the image of the pullback map L2 (Ad(M)) → L2 (M). In particular, we show that the maximal flat Radon transform is injective if and only if M coincides with its adjoint space.",

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AU - Glenn Jackson, Steven

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N2 - Let M be a Riemannian globally symmetric space of compact type, M′ its set of maximal flat totally geodesic tori, and Ad(M) its adjoint space. We show that the kernel of the maximal flat Radon transform τ : L2 (M) → L2 (M′ ) is precisely the orthogonal complement of the image of the pullback map L2 (Ad(M)) → L2 (M). In particular, we show that the maximal flat Radon transform is injective if and only if M coincides with its adjoint space.

AB - Let M be a Riemannian globally symmetric space of compact type, M′ its set of maximal flat totally geodesic tori, and Ad(M) its adjoint space. We show that the kernel of the maximal flat Radon transform τ : L2 (M) → L2 (M′ ) is precisely the orthogonal complement of the image of the pullback map L2 (Ad(M)) → L2 (M). In particular, we show that the maximal flat Radon transform is injective if and only if M coincides with its adjoint space.

KW - Integral geometry

KW - Radon transform

KW - Symmetric space

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M3 - Article

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SN - 0949-5932

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JO - Journal of Lie Theory

JF - Journal of Lie Theory

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ER -

On the kernel of the maximal flat Radon transform on symmetric spaces of compact type

Abstract

ASJC Scopus Subject Areas

Keywords

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