A generalized spectral concentration problem and the varying masks algorithm
<|reference_start|>A generalized spectral concentration problem and the varying masks algorithm: In this paper we generalize the spectral concentration problem as formulated by Slepian, Pollak and Landau in the 1960s. We show that a generalized version with arbitrary space and Fourier masks is well-posed, and we prove some new results concerning general quadratic domains and gaussian filters. We also propose a more general splitting representation of the spectral concentration operator allowing to construct quasi-modes in some situations. We then study its discretization and we illustrate the fact that standard eigen-algorithms are not robust because of a clustering of eigenvalues. We propose a new alternative algorithm that can be implemented in any dimension and for any domain shape, and that gives very efficient results in practice.<|reference_end|>
@article{faou2024a,
    title={A generalized spectral concentration problem and the varying masks
  algorithm},
    author={Erwan Faou (IRMAR, Inria), Yoann Le Henaff},
    journal={arXiv preprint arXiv:2410.01465},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.01465},
    primaryClass={math.NA cs.NA math.SP}
}