Second-Order Parameterizations for the Complexity Theory of Integrable Functions
By: Aras Bacho, Martin Ziegler
Potential Business Impact:
Makes math problems with changing parts easier to solve.
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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