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arXiv · 1603.01988

Invariant subspaces generated by a single function in the polydisc

Beyaz Basak Koca·Nazim Sadik
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Abstract

In this study, we partially answer the question left open in Rudin's book "Function theory in polydiscs" on the structure of invariant subspaces of the Hardy space $H^2(U^n)$ on the polydisc $U^n$. We completely describe all invariant subspaces generated by a single function in the polydisc. Then, using our results, we give the unitary equivalence of this type of invariant subspace and a characterization of outer functions in $H^2(U^n)$.

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Beyaz Basak Koca, Nazim Sadik. 2016-03-07. Invariant subspaces generated by a single function in the polydisc. https://doi.org/10.1134/s0001434617070215

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