Pointwise behavior of SU(1,1) nonlinear Fourier transform

We show that SU(1,1) NLFT can diverge pointwise for square-summable coefficients.

As a consequence, we prove that the classical pointwise asymptotics of polynomials orthogonal on the unit circle can fail for measures in the Szegö class.

We also discuss some special cases when the pointwise convergence holds.