Complementing Nonuniqueness Sets in Model Spaces

It is shown that any incomplete system of reproducing kernels in a model subspace K θ = H 2 ⊖ θH 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 θ can be complemented to a minimal uniqueness set.

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.282 (4), p.473-477
Main Author: Baranov, A. D.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:It is shown that any incomplete system of reproducing kernels in a model subspace K θ = H 2 ⊖ θH 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 θ can be complemented to a minimal uniqueness set.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07192-z