Formulas for the Walsh coefficients of smooth functions and their application to bounds on the Walsh coefficients
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2015
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| _version_ | 1866914175029084160 |
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| author | Suzuki, Kosuke Yoshiki, Takehito |
| author_facet | Suzuki, Kosuke Yoshiki, Takehito |
| contents | We establish formulas for the $b$-adic Walsh coefficients of functions in $C^α[0,1]$ for an integer $α\geq 1$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1504_04131 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Formulas for the Walsh coefficients of smooth functions and their application to bounds on the Walsh coefficients Suzuki, Kosuke Yoshiki, Takehito Numerical Analysis We establish formulas for the $b$-adic Walsh coefficients of functions in $C^α[0,1]$ for an integer $α\geq 1$ 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. |
| title | Formulas for the Walsh coefficients of smooth functions and their application to bounds on the Walsh coefficients |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1504.04131 |