Characterization of Modulation Spaces by Nonlinear Approximation

Details Characterization of Modulation Spaces by Nonlinear Approximation Characterization of Modulation Spaces by Nonlinear Approximation

2006-02-12

arxiv.org/abs/math/0602250v1

Mathematics

Functional Analysis

12 pages

Scientific paper

It is shown that the modulation spaces $M_{p}^{w}$ can be characterized by the approximation behavior of their elements using Local Fourier bases. In analogy to the Local Fourier bases, we show that the modulation spaces can also be characterized by the approximation behavior of their elements using Gabor frames. We derive direct and inverse approximation theorems that describe the best approximation by linear combinations of N terms of a given function using its modulates and translates.

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