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Matematicheskie Zametki, 2017, Volume 102, Issue 2, paper published in the English version journal
(Mi mzm11509)
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This article is cited in 3 scientific papers (total in 3 papers)
Papers published in the English version of the journal
Invariant Subspaces Generated by a Single Function
in the Polydisk
B. Koca, N. Sadik Department of Mathematics, Istanbul University, Istanbul, Turkey
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 $H^2(U^n)$.
Keywords:
invariant subspace, Hardy space, polydisk, outer function, inner
function, unitarily equivalence.
Received: 01.12.2016 Revised: 06.03.2017
Citation:
B. Koca, N. Sadik, “Invariant Subspaces Generated by a Single Function
in the Polydisk”, Math. Notes, 102:2 (2017), 193–197
Linking options:
https://www.mathnet.ru/eng/mzm11509
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