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).