Abstract
For a nonnegative integer α, we study and compute the root functions \({R_{\alpha}^{I}(z, w) = (1-\overline{w}z)^{2+\alpha}K_{\alpha}^{I}(z, w)}\) of finite zero based invariant subspaces I of the weighted Bergman space \({A_{\alpha}^{2}}\) , where \({K_{\alpha}^{I}}\) is the reproducing kernel of I. Furthermore, we estimate ranks of the corresponding root operators.
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Communicated by Scott McCullough.
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López-García, M., López-Salmorán, I. The Root Operator on Finite Zero Based Invariant Subspaces of the Weighted Bergman Space. Complex Anal. Oper. Theory 7, 1231–1238 (2013). https://doi.org/10.1007/s11785-011-0207-5
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DOI: https://doi.org/10.1007/s11785-011-0207-5