Abstract
For a block Hankel operator \(H_\Phi \) with a matrix function symbol \(\Phi \in L^2_{M_{n\times m}}\), it is well-known that \(\ker H_\Phi = \Theta H^2_{\mathbb {C}^r}\) for a natural number r and an \(m\times r\) matrix inner function \(\Theta \) if \(\ker H_\Phi \) is nonempty. It will be shown that the size of the matrix inner function \(\Theta \) associated with \(\ker H_\Phi \) is closely related with a certain degree of independence of the column vectors of \(\Phi \), which will be defined in this paper. As an important application, the shape of shift invariant, or, backward shift invariant subspaces of \(H^2_{\mathbb {C}^n}\) generated by finite elements will be studied.
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Communicated by David Kimsey.
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This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF-2015R1C1A1A01053837). The author appreciates the referee for helpful comments and corrections.
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Kang, DO. Independence of Vector-Valued Functions Associated with Kernels of Block Hankel Operators. Complex Anal. Oper. Theory 13, 4165–4193 (2019). https://doi.org/10.1007/s11785-019-00955-6
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DOI: https://doi.org/10.1007/s11785-019-00955-6