We study the XXZ chain with a boundary at massless regime $-1<Delta<1$. We give the free field realizations of the boundary vacuum state and its dual. Using these realizations, we give the integrable representations of the correlation functions.
Norm inflation implies certain discontinuous dependence of the solution on the initial value. The well-posedness of the mild solution means the existence and uniqueness of the fixed points of the corresponding integral equation. For ${rm BMO}^{-1}$, Auscher-Dubois-Tchamitchian proved that Koch-Tatarus solution is stable. In this paper, we construct a non-Gauss flow function to show that, for classic Navier-Stokes equations, wellposedness and norm inflation may have no conflict and stability may have meaning different to $L^{infty}(({rm BMO}^{-1})^{n})$.
Considering the XXX spin-1/2 chain in the framework of the Algebraic Bethe Ansatz (ABA) we make the following short comment: the product of the creation operators corresponding to the recently found solution of the Bethe equations on the wrong side of the equator (hep-th/9808153) is just zero (not only its action on the pseudovacuum).
We apply a recent result of Borichev-Golinskii-Kupin on the Blaschke-type conditions for zeros of analytic functions on the complex plane with a cut along the positive semi-axis to the problem of the eigenvalues distribution of the Fredholm-type analytic operator-valued functions.