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Stability of the bases and frames reproducing kernels in model spaces

Anton Baranov (2005)

Annales de l'institut Fourier

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

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