Complementing nonuniqueness sets in model spaces
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 50, Tome 512 (2022), pp. 27-34

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It is shown that any incomplete system of reproducing kernels in a model subspace $K_\theta = H^2\ominus \theta H^2$ of the Hardy space $H^2$ can be complemented to a complete and minimal system of reproducing kernels. Thus, any nonuniqueness set for $K_\theta$ can be complemented to a minimal uniqueness set.
@article{ZNSL_2022_512_a2,
     author = {A. D. Baranov},
     title = {Complementing nonuniqueness sets in model spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {27--34},
     publisher = {mathdoc},
     volume = {512},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_512_a2/}
}
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A. D. Baranov. Complementing nonuniqueness sets in model spaces. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 50, Tome 512 (2022), pp. 27-34. http://geodesic.mathdoc.fr/item/ZNSL_2022_512_a2/