Opuscula Math. 44, no. 3 (2024), 359-372
https://doi.org/10.7494/OpMath.2024.44.3.359
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.
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- Hamza El Azhar (corresponding author)
https://orcid.org/0000-0002-3457-3435- Chouaib Doukkali University, Mathematics Department, Faculty of Sciences, Route Ben Maachou, 24000, El Jadida, Morocco
- Abdelouahab Hanine
- 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
- 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.
