Functional analysis behind a Family of Multidimensional Continued Fractions: Part II

The paper proves that, under a domination-by-hypothesis on W and Lh=h, all eigenvalues satisfy −1 ≤ λ ≤ 1 and hence the largest eigenvalue is 1, and it uses a Lasota–Mackey theorem to deduce simplicity under ergodicity. The candidate solution reaches the same conclusions but tightens the eigenvalue bound to |λ| ≤ 1 via an absolute-value/positivity argument and proves simplicity directly by passing to the invariant measure μ = h·m and using ergodicity. Thus both are correct; the model fills minor gaps (complex eigenvalues) and offers an alternative simplicity proof. See Theorem 3 (monotonicity/positivity) and Theorem 4 (domination criterion) in the paper, and the ergodicity-based simplicity statement (Theorem 6) relying on Lasota–Mackey (Theorem 4.2.2) .