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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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$.

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