Second-Order Parameterizations for the Complexity Theory of Integrable Functions

Aras Bacho; Martin Ziegler

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arXiv · 2506.11210

Second-Order Parameterizations for the Complexity Theory of Integrable Functions

Aras Bacho·Martin Ziegler

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Abstract

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.

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Aras Bacho, Martin Ziegler. 2025-06-12. Second-Order Parameterizations for the Complexity Theory of Integrable Functions. https://arxiv.org/abs/2506.11210

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