Compact Toeplitz operators on radial weighted Bergman spaces

What the math gives to ML

The paper gives a constructive compactness criterion for weighted Bergman Toeplitz operators: vanishing of normalized coherent-state quadratic responses at the boundary is equivalent to decay of the operator on high-index frame subspaces. The transferable asset is a resolution-aware regularizer that suppresses localized high-frequency operator action without requiring hard spectral truncation. This is most relevant to attention kernels and neural operators, where controlling high-resolution behavior can improve stability under grid or sequence-length changes. The proposed experiment penalizes both high-index frame tails and normalized responses on localized probe vectors.