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Session III.2 - Approximation Theory

Wednesday, June 21, 17:00 ~ 17:30

Nonlinear wavelet and spline approximation in BMO

Kamen Ivanov

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We present results on two types of nonlinear $n$-term approximation processes: with wavelets in $\operatorname{BMO}({\mathbb R}^d)$ and with splines in $\operatorname{BMO}({\mathbb R})$. Despite the different nature of the wavelets and the splines we are able to show that the similarity of their approximation properties in $L^p$ can be extended to $\operatorname{BMO}$.

Certain Besov-type spaces are naturally involved in these approximation processes. Sharp Jackson and Bernstein estimates are established that allow for a complete characterization of the rates of approximation (approximation spaces).

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