Articles
Kyungpook Mathematical Journal 2018; 58(4): 711-732
Published online December 31, 2018
Copyright © Kyungpook Mathematical Journal.
Multivariable Recursively Generated Weighted Shifts and the 2-variable Subnormal Completion Problem
Kaissar Idrissi, and El Hassan Zerouali*
Centre of Mathematical research in Rabat (CeReMaR), Mohamed V University, Rabat, Morocco
e-mail : kaissar.idrissi@gmail.com and zerouali@fsr.ac.ma
Received: January 6, 2018; Revised: October 16, 2018; Accepted: October 24, 2018
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.