Spectral Properties of Infinitely Smooth Kernel Matrices in the Single Cluster Limit, with Applications to Multivariate Super-Resolution
<|reference_start|>Spectral Properties of Infinitely Smooth Kernel Matrices in the Single Cluster Limit, with Applications to Multivariate Super-Resolution: We study the spectral properties of infinitely smooth multivariate kernel matrices when the nodes form a single cluster. We show that the geometry of the nodes plays an important role in the scaling of the eigenvalues of these kernel matrices. For the multivariate Dirichlet kernel matrix, we establish a criterion for the sampling set ensuring precise scaling of eigenvalues. Additionally, we identify specific sampling sets that satisfy this criterion. Finally, we discuss the implications of these results for the problem of super-resolution, i.e. stable recovery of sparse measures from bandlimited Fourier measurements.<|reference_end|>
@article{diab2024spectral,
    title={Spectral Properties of Infinitely Smooth Kernel Matrices in the Single
  Cluster Limit, with Applications to Multivariate Super-Resolution},
    author={Nuha Diab and Dmitry Batenkov},
    journal={arXiv preprint arXiv:2407.10600},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.10600},
    primaryClass={math.NA cs.NA math.SP}
}