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Invariant subspaces generated by a single function in the Polydisk

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Abstract

In this study, we partially answer a question left open in Rudin’s book “Function Theory in Polydisks” on the structure of invariant subspaces of the Hardy space H 2(U n) on the polydisk U n. We completely describe all invariant subspaces generated by a single function in the polydisk. Then, using our results, we prove the unitary equivalence of this type of invariant subspace and a characterization of outer functions in H 2(U n).

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Authors and Affiliations

  1. Department of Mathematics, Istanbul University, Istanbul, Turkey

    B. B. Koca & N. Sadik

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  1. B. B. Koca
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  2. N. Sadik
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Correspondence to B. B. Koca.

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The article was submitted by the authors for the English version of the journal.

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Koca, B.B., Sadik, N. Invariant subspaces generated by a single function in the Polydisk. Math Notes 102, 193–197 (2017). https://doi.org/10.1134/S0001434617070215

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  • DOI: https://doi.org/10.1134/S0001434617070215

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