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Homogeneous polynomials and invariant subspaces in the polydisc. II


Authors: Takahiko Nakazi and Katsutoshi Takahashi
Journal: Proc. Amer. Math. Soc. 113 (1991), 991-997
MSC: Primary 46J15; Secondary 47A15
DOI: https://doi.org/10.1090/S0002-9939-1991-1069293-9
MathSciNet review: 1069293
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Abstract: We determine the invariant subspaces $ M$ of $ {L^2}({T^2})$ for which there is a subspace $ S$ of $ M$ and a positive integer $ r$ such that

$\displaystyle M = \sum\limits_{n = 0}^\infty { \oplus \left[ {\sum\limits_{j = 0}^n {{z^j}{w^{r(n - j)}}S} } \right]} ,$

where, for a subspace $ A$ of $ {L^2},{T^2},[A]$ denotes the closure of $ A$.

References [Enhancements On Off] (What's this?)

  • [1] V. Mandrekar, The validity of Beurling theorems in polydiscs, Proc. Amer. Math. Soc. 103 (1988), 145-148. MR 938659 (90c:32008)
  • [2] T. Nakazi, Certain invariant subspaces of $ {H^2}$ and $ {L^2}$ on a bidisc, Canad. J. Math. 40 (1988), 1272-1280. MR 973521 (90d:46078)
  • [3] -, Homogeneous polynomials and invariant subspaces in the polydisc, Arch. Math. (to appear).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1069293-9
Article copyright: © Copyright 1991 American Mathematical Society

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