Work

Cantor measures with odd base do not admit Fourier frames

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.08656

Authors: Pont, Jaume de Dios, Liehr, Lukas, Taylor, Mitchell A.

Institution: New York University

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Israel Science Foundation, Azrieli Foundation

Award: G8153456840

OpenAlex ID: W7167944191

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