A Convex Optimization Approach to Learning Koopman Operators

The candidate reproduces Theorem 2’s construction (factor K to obtain y, derive (8)–(9) from (11)–(12), relate G(i) to Hankel blocks) and crucially supplies the missing global-rank step: from r* = rank([G(1); … ; G(N)]) and the identity (H_y)^T H_y = Σ_i G(i), they prove rank(H_y) ≤ r* < r+1, hence (7). The paper’s appendix proof only bounds rank(H_{y(i)}) via rank(G(i)) ≤ r* but does not explicitly justify the stacked Hankel rank (7) for all trajectories; it also does not address cross-trajectory pairs in (11) unless one factors the full K. The model closes both gaps, matching the intended result of Theorem 2. See Problem 2 and Theorem 2 in the paper and the appendix proof snippet cited here: (7)–(9) and (10)–(12) define the setting, and the proof sketch lacks the global stacking argument that the model provides .