Journal article
Rigidity of optimal bases for signal spaces
- Abstract:
-
We discuss optimal L2-approximations of functions controlled in the H1-norm. We prove that the basis of eigenfunctions of the Laplace operator with Dirichlet boundary condition is the only orthonormal basis (bi) of L2 that provides an optimal approximation in the sense of ‖f−∑i=1n(f,bi)bi‖L22≤[Formula presented]∀f∈H01(Ω),∀n≥1. This solves an open problem raised by Y. Aflalo, H. Brezis, A. Bruckstein, R. Kimmel, and N. Sochen...
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- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Authors
Bibliographic Details
- Publisher:
- Elsevier Publisher's website
- Journal:
- Comptes Rendus Mathematique Journal website
- Volume:
- 355
- Issue:
- 7
- Pages:
- 780-785
- Publication date:
- 2017-06-27
- Acceptance date:
- 2017-06-07
- DOI:
- EISSN:
-
1778-3569
- ISSN:
-
1631-073X
Item Description
- Language:
- English
- Keywords:
- Pubs id:
-
1137516
- Local pid:
- pubs:1137516
- Deposit date:
- 2020-11-22
Terms of use
- Copyright holder:
- Académie des sciences
- Copyright date:
- 2017
- Rights statement:
- © 2017 Académie des sciences. Published by Elsevier Masson SAS.
- Notes:
- This is the accepted manuscript version of the article. The final published version is available from Elsevier at https://doi.org/10.1016/j.crma.2017.06.004
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