Homogeneous polynomials and invariant subspaces in the polydisc. II
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- by Takahiko Nakazi and Katsutoshi Takahashi PDF
- Proc. Amer. Math. Soc. 113 (1991), 991-997 Request permission
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 \[ M = \sum \limits _{n = 0}^\infty { \oplus \left [ {\sum \limits _{j = 0}^n {{z^j}{w^{r(n - j)}}S} } \right ]} ,\] where, for a subspace $A$ of ${L^2},{T^2},[A]$ denotes the closure of $A$.References
- V. Mandrekar, The validity of Beurling theorems in polydiscs, Proc. Amer. Math. Soc. 103 (1988), no. 1, 145–148. MR 938659, DOI 10.1090/S0002-9939-1988-0938659-7
- Takahiko Nakazi, Certain invariant subspaces of $H^2$ and $L^2$ on a bidisc, Canad. J. Math. 40 (1988), no. 5, 1272–1280. MR 973521, DOI 10.4153/CJM-1988-055-6 —, Homogeneous polynomials and invariant subspaces in the polydisc, Arch. Math. (to appear).
Additional Information
- © Copyright 1991 American Mathematical Society
- 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