Restriction of eigenfunctions on products of spheres to submanifolds of maximal flats Article Swipe
Let $M$ be a product of rank-one symmetric spaces of compact type, each of dimension at least $3$. We establish sharp $L^p$ bounds for the restriction of Laplace--Beltrami eigenfunctions on $M$ to arbitrary submanifolds contained in a maximal flat, for all $p \ge 2$. The proof combines precise asymptotics of Jacobi polynomials and positivity of Fourier coefficients of spherical functions.
Related Topics
Concepts
Eigenfunction
Mathematics
SPHERES
Product (mathematics)
Dimension (graph theory)
Mathematical analysis
Pure mathematics
Jacobi polynomials
Fourier transform
Fourier analysis
Spherical coordinate system
Spherical mean
Fourier series
Eigenvalues and eigenvectors
Geometry
Upper and lower bounds
Combinatorics
Metadata
- Type
- article
- Landing Page
- http://arxiv.org/abs/2511.14615
- https://arxiv.org/pdf/2511.14615
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7106206880
All OpenAlex metadata
Raw OpenAlex JSON
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- Title
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Restriction of eigenfunctions on products of spheres to submanifolds of maximal flatsWork title
- Type
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articleOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
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2025-11-18Full publication date if available
- Authors
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Zhang YunfengList of authors in order
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https://arxiv.org/abs/2511.14615Publisher landing page
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https://arxiv.org/pdf/2511.14615Direct link to full text PDF
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2511.14615Direct OA link when available
- Concepts
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Eigenfunction, Mathematics, SPHERES, Product (mathematics), Dimension (graph theory), Mathematical analysis, Pure mathematics, Jacobi polynomials, Fourier transform, Fourier analysis, Spherical coordinate system, Spherical mean, Fourier series, Eigenvalues and eigenvectors, Geometry, Upper and lower bounds, CombinatoricsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
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