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Orthonormal bases for α-modulation spaces

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Abstract

We construct an orthonormal basis for the family of bi-variate α-modulation spaces. The construction is based on local trigonometric bases, and the basis elements are closely related to so-called brushlets. As an application, we show thatm-term nonlinear approximation with the representing system in an α-modulation space can be completely characterized.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Aalborg University, Fredrik Bajersvej 7G, DK-9220, Aalborg East, Denmark

    Morten Nielsen

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  1. Morten Nielsen
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Correspondence to Morten Nielsen.

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Nielsen, M. Orthonormal bases for α-modulation spaces. Collect. Math. 61, 173–190 (2010). https://doi.org/10.1007/BF03191240

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