Multivariable Recursively Generated Weighted Shifts and the 2-variable Subnormal Completion Problem

Multivariable Recursively Generated Weighted Shifts and the 2-variable Subnormal Completion Problem

In this paper, we give a new approach to solving the 2-variable subnormal completion problem (SCP for short). To this aim, we extend the notion of recursively generated weighted shifts, introduced by R. Curto and L. Fialkow, to 2-variable case. We next provide "concrete" necessary and suff...

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Veröffentlicht in:Kyungpook mathematical journal 2018, Vol.58 (4), p.711-732
Hauptverfasser: Idrissi, Kaissar, Zerouali, El Hassan
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Zerouali, El Hassan
description In this paper, we give a new approach to solving the 2-variable subnormal completion problem (SCP for short). To this aim, we extend the notion of recursively generated weighted shifts, introduced by R. Curto and L. Fialkow, to 2-variable case. We next provide "concrete" necessary and sufficient conditions for the existence of solutions to the 2-variable SCP with minimal Berger measure. Furthermore, a short alternative proof to the propagation phenomena, for the subnormal weighted shifts in 2-variable, is given.
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title Multivariable Recursively Generated Weighted Shifts and the 2-variable Subnormal Completion Problem
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