대한수학회지 (Journal of the Korean Mathematical Society)

  • 제44권4호
  • /
  • Pages.949-970
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  • 2007
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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COMPLEX MOMENT MATRICES VIA HALMOS-BRAM AND EMBRY CONDITIONS

  • Li, Chunji (INSTITUTE OF SYSTEM SCIENCE COLLEGE OF SCIENCES NORTHEASTERN UNIVERSITY) ;
  • Jung, Il-Bong (DEPARTMENT OF MATHEMATICS COLLEGE OF NATURAL SCIENCES KYUNGPOOK NATIONAL UNIVERSITY) ;
  • Park, Sang-Soo (INSTITUTE OF MATHEMATICAL SCIENCE EWHA WOMANS UNIVERSITY)
  • 발행 : 2007.07.30
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초록

By considering a bridge between Bram-Halmos and Embry characterizations for the subnormality of cyclic operators, we extend the Curto-Fialkow and Embry truncated complex moment problem, and solve the problem finding the finitely atomic representing measure ${\mu}$ such that ${\gamma}_{ij}={\int}\bar{z}^iz^jd{\mu},\;(0{\le}i+j{\le}2n,\;|i-j|{\le}n+s,\;0{\le}s{\le}n);$ the cases of s = n and s = 0 are induced by Bram-Halmos and Embry characterizations, respectively. The former is the Curto-Fialkow truncated complex moment problem and the latter is the Embry truncated complex moment problem.

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참고문헌

  1. R. Curto and L. Fialkow, Solution of the truncated complex moment problems for flat data, Mem. Amer. Math. Soc. 119 (1996), no. 568, x+52pp
  2. R. Curto and L. Fialkow, Flat extensions of positive moment matrices: recursively generated relations, Memoirs Amer. Math. Soc. 136 (1998), no. 648, x+56 pp
  3. R. Curto and L. Fialkow, Solution of the singular quartic moment problem, J. Operator Theory 48 (2002), no. 2, 315-354
  4. M. Embry, A generalization of the Halmos-Bram criterion for subnormality, Acta. Sci. Math. (Szeged) 35 (1973), 61-64
  5. I. Jung, E. Ko, C. Li, and S. Park, Embry truncated complex moment problem, Linear Algebra Appl. 375 (2003), 95-114 https://doi.org/10.1016/S0024-3795(03)00617-7
  6. C. Li, The singular Embry quartic moment problem, Hokkaido Math. J. 34 (2005), no. 3, 655-666 https://doi.org/10.14492/hokmj/1285766290
  7. C. Li and S. Lee, The quartic moment problem, J. Korean Math. Soc. 42 (2005), no. 4, 723-747 https://doi.org/10.4134/JKMS.2005.42.4.723
  8. S. Wolfram, Mathematica, Version 3.0, Wolfram Research Inc., Champaign, IL, 1996

피인용 문헌

  1. A Cyclic Subnormal Completion of Complex Data vol.54, pp.2, 2014, https://doi.org/10.5666/KMJ.2014.54.2.157
  2. ESTIMATING THE DOMAIN OF ATTRACTION VIA MOMENT MATRICES vol.46, pp.6, 2009, https://doi.org/10.4134/BKMS.2009.46.6.1237