Abstract
We study the reproducing kernel Hilbert spaces \(\mathfrak{H}(\mathbb{D}^2 ,{\text{ }}S)\) with kernels of the form
where S(z1,z2) is a Schur function of two variables z 1,z2ℓ\(\mathbb{D}\). They are analogs of the spaces \(\mathfrak{H}\left( {\mathbb{D},S} \right)\) with reproducing kernel (1-S(z)S(w)*)/(1-zw*) introduced by de Branges and Rovnyak l. de Branges and J. Rovnyak, Square Summable Power Series Holt, Rinehart and Winston, New York, 1966. We discuss the characterization of \(\mathfrak{H}(\mathbb{D}^2 ,{\text{ }}S)\) as a subspace of the Hardy space on the bidisk. The spaces \(\mathfrak{H}(\mathbb{D}^2 ,{\text{ }}S)\) form a proper subset of the class of the so–called sub–Hardy Hilbert spaces of the bidisk.
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Alpay, D., Bolotnikov, V., Dijksma, A. et al. Hilbert Spaces Contractively Included in the Hardy Space of the Bidisk. Positivity 5, 25–50 (2001). https://doi.org/10.1023/A:1009826406222
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DOI: https://doi.org/10.1023/A:1009826406222