Let μ be an even measure on the real line R such that c_{1 R} |f |² dx _R |f |² dμ c_{2 R} |f |² dx for all functions f in the Paley–Wiener space PW_a. We prove that μ is the spectral measure for the unique Hamiltonian H = ^w _{0 w} ⁰1 on [0, a] generated by a weight w from the Muckenhoupt class A₂[0, a]. As a consequence of this result, we construct Krein’s orthogonal entire functions with respect to μ and prove that every positive, bounded, invertible Wiener–Hopf operator on [0, a] with real symbol admits triangular factorization.