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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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Publisher copy:
10.1016/j.crma.2017.06.004

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0001-8360-3250
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
Language:
English
Keywords:
Pubs id:
1137516
Local pid:
pubs:1137516
Deposit date:
2020-11-22

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