Brangesian spaces in the polydisk

Singh, Dinesh

doi:10.1090/S0002-9939-1990-1028289-2

Brangesian spaces in the polydisk
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Proc. Amer. Math. Soc. 110 (1990), 971-977 Request permission

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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