Restricted Non-linear Approximation in Sequence Spaces and Applications to Wavelet Bases and Interpolation
نویسنده
چکیده
Restricted non-linear approximation is a type of N-term approximation where a measure ν on the index set (rather than the counting measure) is used to control the number of terms in the approximation. We show that embeddings for restricted non-linear approximation spaces in terms of weighted Lorentz sequence spaces are equivalent to Jackson and Bernstein type inequalities, and also to the upper and lower Temlyakov property. As applications we obtain results for wavelet bases in Triebel-Lizorkin spaces by showing the Temlyakow property in this setting. Moreover, new interpolation results for Triebel-Lizorkin and Besov spaces are obtained.
منابع مشابه
Non-linear Approximation and Interpolation Spaces
We study n-term wavelet-type approximations in Besov and Triebel–Lizorkin spaces. In particular, we characterize spaces of functions which have prescribed degree of n-term approximation in terms of interpolation spaces. These results are applied to identify interpolation spaces between Triebel–Lizorkin and Besov spaces.
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