For fractional Gaussian covariance operators satisfying (K_alpha psi)(x) = -lambda psi''(x), the eigenvalues obey lambda_n = C (pi n - c_alpha - kappa pi/(3-alpha) + O(n^{-1}))^{alpha-3}, and the same formula persists when a potential term is added.
Quantitative analysis in Sobolev imbed- ding theorems and applications to spectral theory
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Spectral asymptotics for a class of integro-differential equations arising in the theory of fractional Gaussian processes
For fractional Gaussian covariance operators satisfying (K_alpha psi)(x) = -lambda psi''(x), the eigenvalues obey lambda_n = C (pi n - c_alpha - kappa pi/(3-alpha) + O(n^{-1}))^{alpha-3}, and the same formula persists when a potential term is added.