Cantor measures with odd base do not admit Fourier frames

Jaume de Dios Pont; Lukas Liehr; Mitchell A. Taylor

Cantor measures with odd base do not admit Fourier frames

Functional Analysis 2026-07-09 v1

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

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.

Cite

@article{arxiv.2607.08656,
  title  = {Cantor measures with odd base do not admit Fourier frames},
  author = {Jaume de Dios Pont and Lukas Liehr and Mitchell A. Taylor},
  journal= {arXiv preprint arXiv:2607.08656},
  year   = {2026}
}

Comments

Lean verification available at https://github.com/jaumededios/Cantor_Measure_Frames