Rigidity of optimal bases for signal spaces
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27/07/2017Estado
info:eu-repo/semantics/publishedVersionMetadatos
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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 projections.
This solves an open problem raised by Y. Aflalo, H. Brezis, A. Bruckstein, R. Kimmel, and N. Sochen (Best bases for signal spaces, C. R. Acad. Sci. Paris, Ser. I 354 (12) (2016) 1155 1167). 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 projections.
This solves an open problem raised by Y. Aflalo, H. Brezis, A. Bruckstein, R. Kimmel, and N. Sochen (Best bases for signal spaces, C. R. Acad. Sci. Paris, Ser. I 354 (12) (2016) 1155 1167).
Rigidity of optimal bases for signal spaces
Tipo de Actividad
Artículos en revistasISSN
1631-073XPalabras Clave
optimal basis, L2 projections, eigenfunctions, Laplace operatoroptimal basis, L2 projections, eigenfunctions, Laplace operator