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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Brangesian spaces in the polydisk


Author: Dinesh Singh
Journal: Proc. Amer. Math. Soc. 110 (1990), 971-977
MSC: Primary 46E20; Secondary 32A10, 47A15, 47B38
MathSciNet review: 1028289
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Abstract: In this paper we extend to the polydisk $ {D^2}$ a theorem of L. de Branges which characterizes the class of all Hilbert spaces that are contractively contained in the classical Hardy space $ {H^2}$ of the disk and which are invariant under the shift $ S$ acting as an isometry. Our theorem characterizes Hilbert spaces which are vector subspaces of $ {H^2}({D^2})$ and which are invariant under the operators of multiplication by the coordinate functions whose actions are isometric and which doubly commute. We do not use contractivity.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1028289-2
PII: S 0002-9939(1990)1028289-2
Keywords: Polydisk, de Branges's theorem
Article copyright: © Copyright 1990 American Mathematical Society