Abstract
For an invariant subspace $I$ of the Bergman space we study an integral operator on $I$ defined in terms of the reproducing kernel of $I$. Such an operator will be called the root operator of $I$ and its associated integral kernel will be called the root function of $I$. We obtain fundamental spectral properties of the root operator when the invariant subspace $I$ has finite index.
Citation
Rongwei Yang. Kehe Zhu. "The root operator on invariant subspaces of the Bergman space." Illinois J. Math. 47 (4) 1227 - 1242, Winter 2003. https://doi.org/10.1215/ijm/1258138101
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