Stability of bases and frames of reproducing kernels in model spaces

We study the bases and frames of reproducing kernels in the model subspaces K-circle minus(2) = H-2 circle minus circle minus H-2 of the Hardy class H2 in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels k(lambda n) (z) = (1 - <(circle minus(lambda(n)))over bar >circle minus(z))/(z-(lambda) over bar (n)) under "small" perturbations of the points lambda(n). We propose an approach to this problem based on the recently obtained estimates of derivatives in the spaces K-circle minus(2) and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.