Space-time POD and the Hankel matrix

The paper proves that (i) the weighted SVD of the Hankel data matrix yields the discrete space–time POD eigenpairs, and (ii) space–time POD converges to space-only POD as T→0 and to SPOD as T→∞. The candidate solution reproduces these results with the same core SVD–eigendecomposition identity and the standard stationarity + convolution/Fourier argument. The only substantive difference is that the candidate makes the per-unit-time scaling explicit in the long-time limit (λ(T)/T), which is consistent with the paper’s formulations and its short-time linear-in-T scaling, though the paper does not emphasize this normalization in its long-time derivation. No contradictions were found; assumptions (time-independent weight, WSS/ergodicity, square-integrability) are aligned.