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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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Keywords: Polydisk, de Branges's theorem
Article copyright: © Copyright 1990 American Mathematical Society

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