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Solution of the y=x3 truncated moment problem
by
Lawrence Fialkow
SUNY New Paltz
Let b = (bij) (i, j ≥ 0, i+j ≤ 2n) denote a real bisequence of degree 2n. In previous work with R.E. Curto, we showed that b has a representing measure supported in a planar algebraic curve of degree one or two, p(x, y) = 0, if and only if the associated moment matrix M(n)(b) is positive, recursively generated, has a column dependence relation p(X, Y) = 0, and satisfies the "variety condition". In the present work we solve the corresponding problem for measures supported in y = x3, and we show that some essentially new phenomena arise; in particular, the solution is partly algorithmic.
Date received: February 1, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavq-30.