Asymptotic behavior of the eigenvalues of certain integral equations. II

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Gradient-Based Kernel Dimension Reduction for Regression (2014, background): “It is known that the eigenspectrum of Gram matrices with Gaussian kernel decays fast for some typical data distributions (Widom 1963, 1964), so that the low-rank approximation can give good approximation accuracy with significant saving of the computational cost.”
Kernel independent component analysis (2003, background): “Widom (1963, 1964) provides some useful results regarding the spectra of the operator T dened in Eq. (25) for translation-invariant kernels of the form k(x y). He shows that the rate of decay of the spectrum depends only on the rate of decay of the Fourier tranform (!) of k, and of the rate of deca”
Kernel Bayes' rule: Bayesian inference with positive definite kernels (2013, background): “It is known that in some typical cases the eigenspectram of a Gram matrix decays fast (Widom, 1963, 1964; Bach and Jordan, 2002).”