Physical Sciences and Mathematics Commons^™

Bernstein And Bernstein-Like Inequalities For Modulation Spaces, Sa'ud Al-Sa'di, Salti Samarah

International Journal of Emerging Multidisciplinaries: Mathematics

It is shown that the modulation spaces Mwp 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.