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arXiv · 2607.08656

Cantor measures with odd base do not admit Fourier frames

Jaume de Dios Pont·Lukas Liehr·Mitchell A. Taylor
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Abstract

We prove that the Cantor measure with base $b$ does not admit a Fourier frame whenever $b > 1$ is an odd integer. In particular, this answers a question of Strichartz on the existence of a Fourier frame for the middle third Cantor measure. A formalization of our main result in Lean 4 is also provided.

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Jaume de Dios Pont, Lukas Liehr, Mitchell A. Taylor. 2026-07-09. Cantor measures with odd base do not admit Fourier frames. https://arxiv.org/abs/2607.08656

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