The Quartic Complex Moment Problem
by
Lawrence Fialkow
SUNY New Paltz
Coauthors: R.E. Curto

For complex numbers \gamma_ij, 0 <= i+j <= 4, we present concrete conditions for the existence of a positive Borel measure \mu, supported in the complex plane, such that \gamma_ij = \int  [`z]ⁱz^j d\mu. We use extensions of positive moment matrices to explicitly construct finitely atomic representing measures having the fewest possible atoms.

Date received: April 15, 1999