Wavelet characterization of exponentially weighted Besov space with dominating mixed smoothness and its application to function approximation

09/12/2022

∙

by   Yoshihiro Kogure, et al.

∙

0

∙

share

Although numerous studies have focused on normal Besov spaces, limited studies have been conducted on exponentially weighted Besov spaces. Therefore, we define exponentially weighted Besov space VB_p,q^δ,w(ℝ^d) whose smoothness includes normal Besov spaces, Besov spaces with dominating mixed smoothness, and their interpolation. Furthermore, we obtain wavelet characterization of VB_p,q^δ,w(ℝ^d). Next, approximation formulas such as sparse grids are derived using the determined formula. The results of this study are expected to provide considerable insight into the application of exponentially weighted Besov spaces with mixed smoothness.