Fourier frames for the surface measure on the sphere

Title:Fourier frames for the surface measure on the sphere

Speaker:刘博辰(南方科技大学)

Time:Monday, October 6, 2025, 10:00-11:00

Venue: 明德楼B201-1

Abstract:It is known that a small spherical cap (rigorously its surface measure) admits Fourier frames, while the whole sphere does not. We prove more general results. Consequences indclude that a small spherical cap in $\mathbb{R}^d$ near the north pole cannot have a frame spectrum near the $x_d$-axis, and $S$ does not admit any Fourier frame if its interior contains a closed hemisphere. We also resolve the endpoint case, that is, a hemisphere does not admit any Fourier frame. Our results also hold on more general smooth surfaces with nonvanishing Gaussian curvature.