Annals of Functional Analysis

A new approach to the nonsingular cubic binary moment problem

Raúl E. Curto and Seonguk Yoo

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We present an alternative solution to nonsingular cubic moment problems, using techniques that are expected to be useful for higher-degree truncated moment problems. In particular, we apply the theory of recursively determinate moment matrices to deal with a case of rank-increasing moment matrix extensions.

Article information

Ann. Funct. Anal., Volume 9, Number 4 (2018), 525-536.

Received: 7 August 2017
Accepted: 4 December 2017
First available in Project Euclid: 15 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 47A30: Norms (inequalities, more than one norm, etc.) 15A83: Matrix completion problems 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05] 15A48

cubic moment problem recursively determinate moment matrix flat extension semidefinite programming


Curto, Raúl E.; Yoo, Seonguk. A new approach to the nonsingular cubic binary moment problem. Ann. Funct. Anal. 9 (2018), no. 4, 525--536. doi:10.1215/20088752-2017-0066.

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  • [1] 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.
  • [2] R. E. Curto and L. A. Fialkow, Flat extensions of positive moment matrices: Recursively generated relations, Mem. Amer. Math. Soc. 136 (1998), no. 648.
  • [3] R. E. Curto and L. A. Fialkow, “Flat extensions of positive moment matrices: Relations in analytic or conjugate terms” in Nonselfadjoint Operator Algebras, Operator Theory, and Related Topics, Oper. Theory Adv. Appl. 104. Birkhäuser, Basel, 1998, 59–82.
  • [4] R. E. Curto and L. A. Fialkow, Solution of the singular quartic moment problem, J. Operator Theory 48 (2002), no. 2, 315–354.
  • [5] R. E. Curto and L. A. Fialkow, Recursively determined representing measures for bivariate truncated moment sequences, J. Operator Theory 70 (2013), no. 2, 401–436.
  • [6] R. E. Curto, L. A. Fialkow, and H. M. Möller, The extremal truncated moment problem, Integral Equations Operator Theory 60 (2008), no. 2, 177–200.
  • [7] R. E. Curto, S. H. Lee, and J. Yoon, A new approach to the 2-variable subnormal completion problem, J. Math. Anal. Appl. 370 (2010), no. 1, 270–283.
  • [8] R. E. Curto and S. Yoo, Concrete solution to the nonsingular binary quartic moment problem, Proc. Amer. Math. Soc. 144 (2016), no. 1, 249–258.
  • [9] L. A. Fialkow and J. Nie, Positivity of Riesz functionals and solutions of quadratic and quartic moment problems, J. Funct. Anal. 258 (2010), no. 1, 328–356.
  • [10] D. P. Kimsey, The cubic complex moment problem, Integral Equations Operator Theory 80 (2014), no. 3, 353–378.
  • [11] D. P. Kimsey, The subnormal completion problem in several variables, J. Math. Anal. Appl. 434 (2016), no. 2, 1504–1532.
  • [12] D. P. Kimsey, Matrix-valued moment problems, Ph.D. dissertation, Drexel University, Philadelphia, PA, 2011.
  • [13] D. P. Kimsey and H. Woerdeman, The truncated matrix-valued $K$-moment problem on $\mathbb{R}^{d}$, $\mathbb{C}^{d}$, and $\mathbb{T}^{d}$, Trans. Amer. Math. Soc. 365 (2013), no. 10, 5393–5430.
  • [14] Y. L. Šmul’jan, An operator Hellinger integral (in Russian), Mat. Sb. 49 (91) (1959), 381–430; English translation in Amer. Math. Soc. Transl. Ser 2 22 (1962), 289–337.
  • [15] Wolfram Research, Mathematica, Version 9.0, Champaign, Ill., 2013.