Formulas for the Walsh coefficients of smooth functions and their application to bounds on the Walsh coefficients

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• 作者：Kosuke Suzuki ; ^{kosuke.suzuki1@unsw.edu.au" class="auth_mail" title="E-mail the corresponding author} ; Takehito Yoshiki ^{takehito.yoshiki1@unsw.edu.au" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Walsh series ; Walsh coefficient ; Sobolev space ; Smooth function
• 刊名：Journal of Approximation Theory
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：205
• 期：Complete
• 页码：1-24
• 全文大小：288 K

文摘

We establish formulas for the b$b$-adic Walsh coefficients of functions in C^α[0,1]$C^{\alpha }[0,1]$ for an integer α≥1$\alpha \ge 1$ and give upper bounds on the Walsh coefficients of these functions. We also study the Walsh coefficients of periodic and non-periodic functions in reproducing kernel Hilbert spaces.