论文标题
小波表征指数加权的BESOV空间，具有主导的混合光滑度及其在功能近似的应用
Wavelet characterization of exponentially weighted Besov space with dominating mixed smoothness and its application to function approximation
论文作者
论文摘要
尽管大量研究集中在正常的BESOV空间上，但对成倍加权的BESOV空间进行了有限的研究。因此，我们定义了指数加权的besov空间$ vb_ {p，q}^{δ，w}（\ mathbb {r}^d）$，其平滑度包括正常的besov空间，besov空间具有统治混合平滑度和插值。此外，我们获得了$ vb_ {p，q}^{δ，w}（\ mathbb {r}^d）$的小波表征。接下来，使用确定的公式得出近似公式，例如稀疏网格。预计这项研究的结果将对具有混合光滑度的指数加权BESOV空间的应用提供大量见解。
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 $VB_{p,q}^{δ,w}(\mathbb{R}^d)$ whose smoothness includes normal Besov spaces, Besov spaces with dominating mixed smoothness, and their interpolation. Furthermore, we obtain wavelet characterization of $VB_{p,q}^{δ,w}(\mathbb{R}^d)$. 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.
