Opuscula Math. 44, no. 3 (2024), 359-372

Opuscula Mathematica

A note on the general moment problem

Hamza El Azhar
Abdelouahab Hanine
El Hassan Zerouali

Abstract. 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 \(\mathbb{R}_+\).

Keywords: general moment problem, charge sequences, atomic measure.

Mathematics Subject Classification: 44A60.

Full text (pdf)

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  • Hamza El Azhar (corresponding author)
  • ORCID iD https://orcid.org/0000-0002-3457-3435
  • Chouaib Doukkali University, Mathematics Department, Faculty of Sciences, Route Ben Maachou, 24000, El Jadida, Morocco
  • Abdelouahab Hanine
  • ORCID iD https://orcid.org/0009-0009-6988-3634
  • Mohammed V University in Rabat, Mathematics Department, Faculty of Sciences, 4 Avenue Ibn Battouta, B.P. 1014 RP, Rabat, Morocco
  • El Hassan Zerouali
  • ORCID iD https://orcid.org/0000-0001-6240-7859
  • 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
  • Communicated by P.A. Cojuhari.
  • Received: 2023-01-06.
  • Revised: 2023-10-17.
  • Accepted: 2023-11-11.
  • Published online: 2024-02-15.
Opuscula Mathematica - cover

Cite this article as:
Hamza El Azhar, Abdelouahab Hanine, El Hassan Zerouali, A note on the general moment problem, Opuscula Math. 44, no. 3 (2024), 359-372, https://doi.org/10.7494/OpMath.2024.44.3.359

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