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math.CA2025
Fourier frames on smooth surfaces with nonvanishing Gaussian curvature
Xinyu Chen, Bochen Liu
It is known that a small spherical cap (rigorously its surface measure) admits Fourier frames, while the whole sphere does not. In this paper, we prove more general results. Conseq…
math.CA2025
Fourier Frames on Salem Measures
Longhui Li, Bochen Liu
For every we construct -dimensional Salem measures in the unit interval that do not admit any Fourier frame. Our examples are generic for each , including all exi…
math.CA2024
Dimension of Diophantine approximation and some applications in harmonic analysis
Longhui Li, Bochen Liu
In this paper we construct a new family of sets based on Diophantine approximation in the Euclidean space, and consider their applications in several problems in harmonic analysis.…