Editing Moment problem (section)

== Introduction ==

In the classical setting, <math>\mu</math> is a measure on the [[real line]], and <math>M</math> is the sequence <math>\{x^n : n=1,2,\dotsc\}</math>. In this form the question appears in [[probability theory]], asking whether there is a  [[probability measure]] having specified [[mean]], [[variance]] and so on, and whether it is unique.

There are three named classical moment problems: the [[Hamburger moment problem]] in which the [[support (mathematics)|support]] of <math>\mu</math> is allowed to be the whole real line; the [[Stieltjes moment problem]], for <math>[0,\infty)</math>; and the [[Hausdorff moment problem]] for a bounded interval, which [[without loss of generality]] may be taken as <math>[0,1]</math>.

The moment problem also extends to [[complex analysis]] as the [[trigonometric moment problem]] in which the Hankel matrices are replaced by [[Toeplitz matrices]] and the support of {{math|''&mu;''}} is the [[Circle group|complex unit circle]] instead of the real line.{{sfn | Schmüdgen | 2017 | p=257}}