Solvability of time-varying infinite-dimensional linear port-Hamiltonian systems

The paper’s Theorem V.2 proves that when B, C, D are bounded and dom([A B; C D]) = dom(A) × E with ψ = I (so E = F), then [A B; C D] is a system node and, under (III.1), V = V× = [P(0)^{-1} dom(A); H^1_loc] (the proof explicitly computes the external Cayley transform and shows dom(A×) = dom(A)) . The candidate solution establishes the same two claims: (i) A is m-dissipative (hence generates a C0-semigroup) via a resolvent/Schur-complement argument, and (ii) V = V× with the same characterization. One technical slip is the model’s explicit formula for dom([A B; C D]^×): it omits a factor √(2Re β) in the second component induced by the domain map in (III.4)–(III.5) . This mis-scaling does not affect the final conclusion because the paper shows directly that the Cayley-transformed realization has the same domain as [A B; C D] and that dom(A×) = dom(A), which implies the claimed V× characterization . Overall, both reach the correct results; the proofs are different (adjoint-dissipativity vs. Schur-complement), and the model needs a minor domain-factor correction.