Abstract
We prove that the exponential localization of a frame with respect to an orthonormal basis in a Hilbert space is not sufficient to get a Bernstein inequality. In other words, the fact that a function belongs to an approximation space of the frame cannot be characterized in terms of the sparseness of its frame coefficients.
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Gribonval, R., Nielsen, M. On a Problem of Gröchenig About Nonlinear Approximation with Localized Frames. J. Fourier Anal. Appl. 10, 433–437 (2004). https://doi.org/10.1007/s00041-004-3072-z
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DOI: https://doi.org/10.1007/s00041-004-3072-z