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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.11210 |
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| _version_ | 1866912427358027776 |
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| author | Bacho, Aras Ziegler, Martin |
| author_facet | Bacho, Aras Ziegler, Martin |
| contents | We develop a unified second-order parameterized complexity theory for spaces of integrable functions. This generalizes the well-established case of second-order parameterized complexity theory for spaces of continuous functions. Specifically we prove the mutual linear equivalence of three natural parameterizations of the space $\Lrm{p}$ of $p$-integrable complex functions on the real unit interval: (binary) $\Lrm{p}$-modulus, rate of convergence of Fourier series, and rate of approximation by step functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Second-Order Parameterizations for the Complexity Theory of Integrable Functions Bacho, Aras Ziegler, Martin Computational Complexity We develop a unified second-order parameterized complexity theory for spaces of integrable functions. This generalizes the well-established case of second-order parameterized complexity theory for spaces of continuous functions. Specifically we prove the mutual linear equivalence of three natural parameterizations of the space $\Lrm{p}$ of $p$-integrable complex functions on the real unit interval: (binary) $\Lrm{p}$-modulus, rate of convergence of Fourier series, and rate of approximation by step functions. |
| title | Second-Order Parameterizations for the Complexity Theory of Integrable Functions |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2506.11210 |