The λ-cosine transforms, differential operators, and Funk transforms on Stiefel and Grassmann manifolds

B. Rubin

doi:10.1016/j.aim.2021.108022

The λ-cosine transforms, differential operators, and Funk transforms on Stiefel and Grassmann manifolds

B. Rubin

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

3 Scopus citations

Abstract

We introduce a new family of invariant differential operators associated with λ-cosine and Funk-Radon transforms on Stiefel and Grassmann manifolds. These operators reduce the order of the λ-cosine transforms and yield new inversion formulas. Intermediate Funk-cosine transforms corresponding to integration over matrices of lower rank are studied. The main tools are polar decomposition and Fourier analysis on matrix space.

Original language	English
Article number	108022
Journal	Advances in Mathematics
Volume	392
DOIs	https://doi.org/10.1016/j.aim.2021.108022
State	Published - 3 Dec 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

Differential operators
Funk-Radon transforms
Grassmann manifolds
Stiefel manifolds
λ-cosine transforms

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10.1016/j.aim.2021.108022

Cite this

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abstract = "We introduce a new family of invariant differential operators associated with λ-cosine and Funk-Radon transforms on Stiefel and Grassmann manifolds. These operators reduce the order of the λ-cosine transforms and yield new inversion formulas. Intermediate Funk-cosine transforms corresponding to integration over matrices of lower rank are studied. The main tools are polar decomposition and Fourier analysis on matrix space.",

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AB - We introduce a new family of invariant differential operators associated with λ-cosine and Funk-Radon transforms on Stiefel and Grassmann manifolds. These operators reduce the order of the λ-cosine transforms and yield new inversion formulas. Intermediate Funk-cosine transforms corresponding to integration over matrices of lower rank are studied. The main tools are polar decomposition and Fourier analysis on matrix space.

KW - Differential operators

KW - Funk-Radon transforms

KW - Grassmann manifolds

KW - Stiefel manifolds

KW - λ-cosine transforms

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JO - Advances in Mathematics

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The λ-cosine transforms, differential operators, and Funk transforms on Stiefel and Grassmann manifolds

Abstract

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Keywords

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