The classical
moment problem of Hausdorff
is relevant in probability theory or spectral problems of selfadjoint
operators. An open problem:
Given an arbitrary Borel measure on the square X=[0,1] x [0,1].
Assume you know the expectation values of
(x,y) -> x ^{ n }
y ^{ m } (= moments)
How does one decide from these moments,
whether the measure is absolutely continuous? How can one
decide whether mutual absolutely continuity holds for
two given measures, if their moments are known?