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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Finite-codimensional invariant subspaces of Bergman spaces


Authors: Sheldon Axler and Paul Bourdon
Journal: Trans. Amer. Math. Soc. 306 (1988), 805-817
MSC: Primary 46E15; Secondary 32A10, 32H20, 46J15, 47B38
MathSciNet review: 933319
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Abstract: For a large class of bounded domains in $ \mathbb{C}$, we describe those finite codimensional subspaces of the Bergman space that are invariant under multiplication by $ z$. Using different techniques for certain domains in $ {\mathbb{C}^N}$, we describe those finite codimensional subspaces of the Bergman space that are invariant under multiplication by all the coordinate functions.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0933319-5
PII: S 0002-9947(1988)0933319-5
Article copyright: © Copyright 1988 American Mathematical Society