Multivariable Recursively Generated Weighted Shifts and the 2-variable Subnormal Completion Problem
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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.
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.
참고문헌 (13)
- C. Bayer, "The proof of Tchakaloff’s theorem", Proc. Amer. Math. Soc., 134, pp.3035~3040 (2006)
- R. Ben Taher, "Recursive subnormal completion and the truncated moment problem", Bull. London Math. Soc., 33, pp.425~432 (2001)
- R. Curto, "Recursively generated weighted shifts and the subnormal completion problem", Integral Equations Operator Theory, 17(2), pp.202~246 (1993)
- R. Curto, "Recursively generated weighted shifts and the subnormal completion problem II", Integral Equations and Operator Theory, 18(4), pp.369~426 (1994)
- R. E. Curto, "Solution of the truncated complex moment problem for flat data", Mem. Amer. Math. Soc, 119(568), pp.52~ (1996)
- R. E. Curto, "Flat extensions of positive moment matrices: Recursively generated relations", Mem. Amer. Math. Soc, 136(648), pp.56~ (1998)
- R. E. Curto, "The truncated complex K-moment problem", Trans. Amer. Math. Soc, 352, pp.2825~2855 (2000)
- R. Curto, "A new approach to the 2-variable subnormal completion problem", J. Math. Anal. Appl, 370, pp.270~283 (2010)
- F. Dubeau, "On Weighted r-Generalized Fibonacci Sequences", Fibonacci Quart, 35(2), pp.102~110 (1997)
- N.P. Jewell, "Commuting weighted shifts and analytic function theory in several variables", J. Operator Theory, 1, pp.207~223 (1979)
- S. H. Lee, "Recursiveness and propagation for 2-variable weighted shifts", Linear Algebra Appl, 504, pp.228~247 (2016)
- J.L. Smuljan, "An operator Hellinger integral (Russian)", Mat. Sb., 91, pp.381~430 (1959)
- J. Stampfli, "Which weighted shifts are subnormal?", Pacific J. Math, 17, pp.367~379 (1966)