Dimensional stability in truncated moment problems

An approach to truncated moment problems is developed, via the Riesz functional and an assumed dimensional stability of its associated Hilbert spaces. Although equivalent to a concept of “flatness” introduced by R. Curto and L. Fialkow, the dimensional stability discussed in this paper has a different geometric aspect and leads to statements parallel to those of the quoted authors, as well as to some newer ones, obtained by simpler arguments. A stability equation, giving a local characterization of the dimensional stability, is also presented.