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http://dx.doi.org/10.5666/KMJ.2018.58.4.711

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

Idrissi, Kaissar (Centre of Mathematical research in Rabat (CeReMaR), Mohamed V University)
Zerouali, El Hassan (Centre of Mathematical research in Rabat (CeReMaR), Mohamed V University)
Publication Information
Kyungpook Mathematical Journal / v.58, no.4, 2018 , pp. 711-732 More about this Journal
Abstract
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.
Keywords
subnormal completion problem; multivariable weighted shift; generalized Fibonacci sequence; moment problems; propagation phenomena;
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