Revista Matemática Iberoamericana


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Volume 29, Issue 1, 2013, pp. 115–134
DOI: 10.4171/RMI/715

Phase space localization of Riesz bases for $L^2(\mathbb{R}^d)$

Karlheinz Gröchenig[1] and Eugenia Malinnikova[2]

(1) Institut für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090, WIEN, AUSTRIA
(2) Department of Mathematics, Norwegian University of Science and Technology, 7491, TRONDHEIM, NORWAY

We prove a strong uncertainty principle for Riesz bases in $L^2(\mathbb{R}^d)$ and show that the orthonormal basis constructed by Bourgain possesses the optimal phase space localization.

Keywords: Uncertainty principle, Balian–Low theorem, Riesz basis, localized frame

Gröchenig K, Malinnikova E. Phase space localization of Riesz bases for $L^2(\mathbb{R}^d)$. Rev. Mat. Iberoamericana 29 (2013), 115-134. doi: 10.4171/RMI/715