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arXiv · 2603.14904

Signature inversion of $C^1-$axial linear curves

Chong Liu·Shi Wang
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Abstract

We introduce a signature inversion scheme for $C^1$-axial linear curves which are widely used in various areas. We show that in the presence of a linear coordinate function, the derivatives of the underlying curve at any point $x$ can be recovered by tracking the signature coefficients $S_{k,l}$ with $\frac{k}{k+l} \to x$. We furthermore give a quantitative estimates for the convergence rate in this inversion scheme and establish a modulus of continuity of the signature inverse $S^{-1}$ under different topologies by using this inversion procedure.

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Chong Liu, Shi Wang. 2026-03-16. Signature inversion of $C^1-$axial linear curves. https://arxiv.org/abs/2603.14904

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