Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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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)
  • Received : 2018.01.06
  • Accepted : 2018.10.24
  • Published : 2018.12.23
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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.

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Acknowledgement

Supported by : National center of research, Hassan II academy of sciences

References

  1. C. Bayer and J. Teichmann, The proof of Tchakaloff's theorem, Proc. Amer. Math. Soc., 134(2006), 3035-3040. https://doi.org/10.1090/S0002-9939-06-08249-9
  2. R. Ben Taher, M. Rachidi and H. Zerouali, Recursive subnormal completion and the truncated moment problem Bull. London Math. Soc., 33(2001), 425-432. https://doi.org/10.1017/S0024609301008116
  3. R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Integral Equations Operator Theory, 17(2)(1993), 202-246. https://doi.org/10.1007/BF01200218
  4. R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem II, Integral Equations and Operator Theory, 18(4)(1994), 369-426. https://doi.org/10.1007/BF01200183
  5. R. E. Curto and L. A. Fialkow, Solution of the truncated complex moment problem for flat data, Mem. Amer. Math. Soc., 119(1996), no. 568, 52 pp.
  6. R. E. Curto and L. A. Fialkow, Flat extensions of positive moment matrices: Recursively generated relations, Mem. Amer. Math. Soc., 136(1998), no. 648, 56 pp.
  7. R. E. Curto and L. A. Fialkow, The truncated complex K-moment problem, Trans. Amer. Math. Soc., 352(2000), 2825-2855. https://doi.org/10.1090/S0002-9947-00-02472-7
  8. R. Curto, S. H. Lee and J. Yoon, A new approach to the 2-variable subnormal completion problem, J. Math. Anal. Appl., 370(2010), 270-283. https://doi.org/10.1016/j.jmaa.2010.04.061
  9. F. Dubeau, W. Motta, M. Rachidi, and O. Saeki, On Weighted r-Generalized Fibonacci Sequences, Fibonacci Quart., 35(2)(1997), 102-110.
  10. N.P. Jewell and A.R. Lubin, Commuting weighted shifts and analytic function theory in several variables, J. Operator Theory, 1(1979), 207-223.
  11. S. H. Lee and J. Yoon, Recursiveness and propagation for 2-variable weighted shifts, Linear Algebra Appl., 504(2016), 228-247. https://doi.org/10.1016/j.laa.2016.04.006
  12. J.L. Smul'jan, An operator Hellinger integral (Russian), Mat. Sb., 91(1959), 381-430.
  13. J. Stampfli, Which weighted shifts are subnormal?, Pacific J. Math., 17(1966), 367-379. https://doi.org/10.2140/pjm.1966.17.367