On présente ici une approche simple, et plutôt surprenante, des théorèmes de densité de Landau fournissant, pour lʼéchantillonnage et lʼinterpolation, des versions plus fortes des résultats connus. En particulier, on étend le théorème dʼinterpolation au spectre non borné.
We present a surprisingly simple approach to Landauʼs density theorems for sampling and interpolation, which provides stronger versions of these results. In particular, we extend the interpolation theorem to unbounded spectra.
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@article{CRMATH_2012__350_9-10_509_0, author = {Nitzan, Shahaf and Olevskii, Alexander}, title = {Revisiting {Landau's} density theorems for {Paley{\textendash}Wiener} spaces}, journal = {Comptes Rendus. Math\'ematique}, pages = {509--512}, publisher = {Elsevier}, volume = {350}, number = {9-10}, year = {2012}, doi = {10.1016/j.crma.2012.05.003}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.05.003/} }
TY - JOUR AU - Nitzan, Shahaf AU - Olevskii, Alexander TI - Revisiting Landauʼs density theorems for Paley–Wiener spaces JO - Comptes Rendus. Mathématique PY - 2012 SP - 509 EP - 512 VL - 350 IS - 9-10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.05.003/ DO - 10.1016/j.crma.2012.05.003 LA - en ID - CRMATH_2012__350_9-10_509_0 ER -
%0 Journal Article %A Nitzan, Shahaf %A Olevskii, Alexander %T Revisiting Landauʼs density theorems for Paley–Wiener spaces %J Comptes Rendus. Mathématique %D 2012 %P 509-512 %V 350 %N 9-10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.05.003/ %R 10.1016/j.crma.2012.05.003 %G en %F CRMATH_2012__350_9-10_509_0
Nitzan, Shahaf; Olevskii, Alexander. Revisiting Landauʼs density theorems for Paley–Wiener spaces. Comptes Rendus. Mathématique, Tome 350 (2012) no. 9-10, pp. 509-512. doi : 10.1016/j.crma.2012.05.003. http://archive.numdam.org/articles/10.1016/j.crma.2012.05.003/
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☆ Research supported in part by Israel Science Foundation.