A note on the general moment problem

• Autorzy: El Azhar Hamza , Hanine Abdelouahab , Zerouali El Hassan

Identyfikatory

DOI

10.7494/OpMath.2024.44.3.359

• Języki publikacji: EN

Abstrakty

EN

In this note we show that given an indeterminate Hamburger moment sequence, it is possible to perturb the first moment in such way that the obtained sequence remains an indeterminate Hamburger moment sequence. As a consequence we prove that every sequence of real numbers is a moment sequence for a signed discrete measure supported in R+.

Słowa kluczowe

EN

general moment problem; charge sequences; atomic measure

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2024
• Tom: Vol. 44, no. 3
• Strony: 359--372
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

El Azhar Hamza

• Chouaib Doukkali University, Mathematics Department, Faculty of Sciences, Route Ben Maachou, 24000, El Jadida, Morocco

• https://orcid.org/0000-0002-3457-3435

autor

Hanine Abdelouahab

• Mohammed V University in Rabat, Mathematics Department, Faculty of Sciences, 4 Avenue Ibn Battouta, B.P. 1014 RP, Rabat, Morocco

• https://orcid.org/0009-0009-6988-3634

autor

Zerouali El Hassan

• Mohammed V University in Rabat, Mathematics Department, Faculty of Sciences, 4 Avenue Ibn Battouta, B.P. 1014 RP, Rabat, Morocco
• The University of Iowa, Department of Mathematics, 14 MacLean Hall, Iowa City, Iowa, USA

• https://orcid.org/0000-0001-6240-7859

Bibliografia

• [1] N.I. Akheizer, The Classical Moment Problem and Some Related Questions in Analysis, Oliver & Boyd, 1965.
• [2] C. Berg, R. Szwarz, A determinant characterization of moment sequences with finitely many mass points, Linear Multilinear Algebra 63 (2015), 1568–1576.
• [3] R.P. Boas, The Stieltjes moment problem for functions of bounded variation, Bull. Amer. Math. Soc. 45 (1939), 399–404.
• [4] A.J. Duran, The Stieltjes moments problem for rapidly decreasing functions, Proc. Amer. Math. Soc. 107 (1989), 731–741.
• [5] A. Dyachenko, Rigidity of the Hamburger and Stieltjes moment sequences, Constr. Approx. 51 (2020), 441–463.
• [6] H. El-Azhar, K. Idrissi, E.H. Zerouali, Weak positive matrices and hyponormal weighted shifts, Ufa Math. J. 11 (2019), 89–99.
• [7] G.P. Flessas, W.K. Burton, R.R. Whitehead, On the moment problem for non-positive distributions, J. Phys. A: Math. Gen. 15 (1982), 3119–3130.
• [8] M. Frontini, A. Tagliani, Maximum entropy in the generalized moment problem, J. Math. Phys. 39 (1998), 6706–6714.
• [9] H.L. Hamburger, Über eine Erweiterung des Stieltjesschen Momentenproblems, Math. Ann. 82 (1921), 168–187.
• [10] G. Pólya, Sur l’indétermination d’un problème voisin du problème des moments, C. R. Math. Acad. Sci. Paris 207 (1938), 708–711.
• [11] K. Schmüdgen, The Moment Problem, Springer, 2017.
• [12] T.J. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse Math. 8 (1894), 1–122.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)