The paper proves eigenvalue convergence between auto-correlation Hilbert-Schmidt operators and squared coefficients of a time-shift isometry semigroup, plus almost-sure equivalence to the Koopman semigroup under ergodicity.
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Bridging Koopman Operator and time-series auto-correlation based Hilbert-Schmidt operator
The paper proves eigenvalue convergence between auto-correlation Hilbert-Schmidt operators and squared coefficients of a time-shift isometry semigroup, plus almost-sure equivalence to the Koopman semigroup under ergodicity.