East Asian mathematical journal

  • 제40권1호
  • /
  • Pages.25-36
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  • 2024
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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UNIVARIATE TRUNCATED MOMENT PROBLEMS VIA WEAKLY ORTHOGONAL POLYNOMIAL SEQUENCES

  • Seonguk Yoo (Department of Mathematics Education and RINS, Gyeongsang National University)
  • 투고 : 2023.09.06
  • 심사 : 2023.12.13
  • 발행 : 2024.01.31
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초록

Full univariate moment problems have been studied using continued fractions, orthogonal polynomials, spectral measures, and so on. On the other hand, the truncated moment problem has been mainly studied through confirming the existence of the extension of the moment matrix. A few articles on the multivariate moment problem implicitly presented about some results of this note, but we would like to rearrange the important results for the existence of a representing measure of a moment sequence. In addition, new techniques with orthogonal polynomials will be introduced to expand the means of studying truncated moment problems.

키워드

과제정보

The author is deeply grateful to the referees for many suggestions that led to significant improvements in the presentation.

참고문헌

  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. P. Boas, Jr., The Stieltjes moment problem for functions of bounded variation, Bull. Amer. Math. Soc. 45 (1939), no. 6, 399-404. https://doi.org/10.1090/S0002-9904-1939-06992-9
  3. T. S. Chihara, An introduction to orthogonal polynomials, Gordon and Breach Science Publishers, New York-London-Paris, 1978.
  4. R. Curto and L. Fialkow, A. Recursiveness, positivity, and truncated moment problems, Houston J. Math. 17 (1991), no. 4, 603-635.
  5. R. Curto and L. Fialkow, Solution of the truncated complex moment problem for flat data, Mem. Amer. Math. Soc. 119 (1996), no. 568, x+52 pp.
  6. R. Curto, L. Fialkow and H.M. Moller, The extremal truncated moment problem, Integral Equations Operator Theory 60 (2008), 177-200. https://doi.org/10.1007/s00020-008-1557-x
  7. L. Fernandez, T. Perez, and M. Pinar, Weak classical orthogonal polynomials in two variables, J. Comput. Appl. Math. 178 (2005), no.1-2, 191-203. https://doi.org/10.1016/j.cam.2004.08.010
  8. L. Fialkow, Truncated multivariable moment problems with finite variety, J. Operator Theory 60 (2008), 343-377.
  9. L. Fialkow, Solution of the truncated moment problem with variety y = x3, Trans. Amer. Math. Soc. 363 (2011), 3133-3165 https://doi.org/10.1090/S0002-9947-2011-05262-1
  10. G. P. Flessas, W. K. Burton, and R. R. Whitehead, On the moment problem for non-positive distributions, J. Phys. A 15 (1982), no. 10, 3119-3130. https://doi.org/10.1088/0305-4470/15/10/016
  11. R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, 2013.
  12. D. W. Lee, Characterizations of distributional weights for weak orthogonal polynomials satisfying a second-order differential equation, Ann. Mat. Pura Appl. (4) 194 (2015), no.5, 1319-1348. https://doi.org/10.1007/s10231-014-0422-6
  13. K. Schmudgen, The Moment Problem, Springer, 2017. 225-234.
  14. S. Yoo, Sextic moment problems with a reducible cubic column relation, Integral Equations Operator Theory 88 (2017), no. 1, 45-63.  https://doi.org/10.1007/s00020-017-2362-1