A determinant characterization of moment sequences with finitely many mass-points
نویسندگان
چکیده
To a sequence (sn)n≥0 of real numbers we associate the sequence of Hankel matrices Hn = (si+j), 0 ≤ i, j ≤ n. We prove that if the corresponding sequence of Hankel determinants Dn = detHn satisfy Dn > 0 for n < n0 while Dn = 0 for n ≥ n0, then all Hankel matrices are positive semi-definite, and in particular (sn) is the sequence of moments of a discrete measure concentrated in n0 points on the real line. We stress that the conditions Dn ≥ 0 for all n do not imply the positive semi-definiteness of the Hankel matrices. AMS Subject Classification: Primary 44A60; Secondary 15A15
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تاریخ انتشار 2014