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Bibliographic Details
Main Authors: Bacho, Aras, Ziegler, Martin
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2506.11210
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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