Resumen de Orthonormal bases for "alpha"-modulation spaces

Morten Nielsen

• We construct an orthonormal basis for the family of bi-variate $\alpha$-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 that $m$-term nonlinear approximation with the representing system in an $\alpha$-modulation space can be completely characterized.