Fourier frames for odd-base Cantor measures
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The question is whether for every odd integer base b>1, the fair {0,2} base-b Cantor measure admits no Fourier frame. The middle-third case answers Strichartz’s question.
Why it matters and what counts as progress
Why it matters: It asks whether Fourier exponentials can form a stable frame for the middle-third and other odd-base Cantor measures.
What counts as progress: Prove Fourier-frame nonexistence for the stated Cantor measures, or identify a change of base, weights or digit set that permits a frame.
How the problem developed
Palle Jorgensen and Steen Pedersen Constructed Fourier bases for certain Cantor measures and showed that the middle-third Cantor measure has no Fourier basis; this left open whether it admits a Fourier frame.
Robert S. Strichartz Raised the question whether the middle-third Cantor measure admits a Fourier frame.
- 9 Jul 2026 · Reported theorem [4]
Jaume de Dios Pont, Lukas Liehr and Mitchell A. Taylor Claimed that no odd-integer-base Cantor measure admits a Fourier frame, including the middle-third case.
AI contribution
Cantor measures with odd base do not admit Fourier frames
For every odd integer base b>1, the fair {0,2} base-b Cantor measure admits no Fourier frame. The middle-third case answers Strichartz’s question.
Sources
- Palle Jorgensen and Steen Pedersen · Orthogonal harmonic analysis of fractal measures
- Robert S. Strichartz · Mock Fourier series and transforms associated with certain Cantor measures
- D. E. Dutkay, D. Han and Q. Sun · Weighted Fourier frames on self-affine measures
- Jaume de Dios Pont, Lukas Liehr and Mitchell A. Taylor · Cantor measures with odd base do not admit Fourier frames
- Cantor measures with odd base do not admit Fourier frames
- Cantor-frame formalization and review
- Independent Walsh-quotient proof
Website timeline
Publication dates and editorial changes.
AI-suggested obstruction rules out odd-base Cantor Fourier frames