Abstract

In this paper, we deal with solving the Hamburger truncated moment problem without distinction between even and odd case. We establish an algorithm which allows to confirm if a finite sequence is a Hamburger moment sequence or not. This algorithm is generated by linking between the moment problem and Jacobi operators.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 5
Year: 2022

DOI: 10.12732/ijam.v35i5.1

Download Section

Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

1. [1] N. I. Akhiezer, The Classical Moment Problem: and Some Related Questions in Analysis, Oliver and Boyd Ltd., Translation (1965).
2. [2] N. I. Akhiezer and M. G. Krein, Some Questions in the Theory of Mmo- ments, Providence, American Mathematical Society (1962).
3. [3] C. Berg, J. P. R. Christensen, and P. Ressel, Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions, Springer- Verlag, Berlin and Heidelberg (1984).
4. [4] C. Berg and R. Szwarc, A determinant characterization of moment se- quences with finitely many mass-points, Linear Multilinear Algebra, 63, No 8 (2015), 1568-1576.
5. [5] R. E. Curto and L. A. Fialkow, Recursiveness, positivity and truncated moment problems, Houston J. Math., 17 (1991), 603-635.
6. [6] I. S. Iohvidov, Hankel and Toeplitz Matrices and Forms: Algebraic Theory, Math. Social Sci. (1982).
7. [7] Landau, Henry J., Ed. Moments in Mathematics, Amer. Math. Soc., Prov- idence, RI., 37(1987).
8. [8] K. Schmüdgen, The Moment Problem, Springer International Publishing, 277 (2017).
9. [9] J. Stochel, Solving the truncated moment problem solves the full moment problem, Glasgow. Math. J., 43 (2001), 335-341.
10. [10] D. V. Widder, The Laplace Transform, Dover Publications (2010).