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This research aims to understand the eigenvalue behavior of concentration operators in reproducing kernel Hilbert spaces and its implications for discretization schemes.

August 1, 2026Constructive ApproximationOpen Access

Spectral Deviation of Concentration Operators on Reproducing Kernel Hilbert Spaces

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This research aims to understand the eigenvalue behavior of concentration operators in reproducing kernel Hilbert spaces and its implications for discretization schemes.
Studied eigenvalue profiles of concentration operators on reproducing kernel Hilbert spaces.
Investigated the convergence of discrete approximations to continuous spectral profiles.
Demonstrated through Gabor multipliers and short-time Fourier transform (STFT) analyses.
Identified a non-asymptotic relationship between eigenvalues away from 0 and 1 in discrete and continuous cases.
Gabor multipliers on fine grids exhibit spectral deviation estimates consistent with STFT properties.
Localization properties of STFT are effectively observable in practical applications.

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Implication

Randomized analysis of eigenvalues in continuous and discrete settings, suggesting practical localization properties.

Cite This Study

Marceca et al. (2026) studied this question.

synapsesocial.com/papers/6a6d98aae258b358b3c6c49b https://doi.org/10.1007/s00365-026-09768-1

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Spectral Deviation of Concentration Operators on Reproducing Kernel Hilbert Spaces

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Discussion

Implication

Cite This Study

Spectral Deviation of Concentration Operators on Reproducing Kernel Hilbert Spaces

Key Points

Discussion

Implication

Cite This Study

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