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

DOI10.1016/J.JAT.2024.106037arXiv2209.05396OpenAlexW4392640532MaRDI QIDQ6410464

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Publication date: 12 September 2022

Abstract: 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 $V{B}_{p,q}^{delta,w}(mathbb{R}^d)$ whose smoothness includes normal Besov spaces, Besov spaces with dominating mixed smoothness, and their interpolation. Furthermore, we obtain wavelet characterization of $V{B}_{p,q}^{delta,w}(mathbb{R}^d)$. 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.

Full work available at URL: https://doi.org/10.1016/j.jat.2024.106037

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