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The Truncated Moment Problem (TMP) entails finding a positive Borel measure to represent all moments in a finite sequence as an integral; once the sequence admits one or more such measures, it is known that at least one of the measures must be finitely atomic with positive densities (equivalently, a linear combination of Dirac point masses with positive coefficients). On the contrary, there are more general moment problems for which we aim to find a "signed" measure to represent a sequence; that is, the measure may have some negative densities. This type of problem is referred to as the General Truncated Moment Problem (GTMP). The Jordan Decomposition Theorem states that any (signed) measure can be written as a difference of two positive measures, and hence, in the view of this theorem, we are able to apply results for TMP to study GTMP. In this note we observe differences between TMP and GTMP; for example, we cannot have an analogous to the Flat Extension Theorem for GTMP. We then present concrete solutions to lower-degree problems.
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참고문헌 (14)
참고문헌 신청
R. P. Boas / 1939 / The Stieltjes moment problem for functions of bounded variation / Bull. Amer. Math. Soc 45(6):399~404
R. Curto / 1991 / Recursiveness, positivity, and truncated moment prob-lems / Houston J. Math 17(4):603~635
R. Curto / 2008 / An analogue of the Riesz-Haviland theorem for the truncated moment problem / J. Funct. Anal 255(10):2709~2731
R. Curto / 2008 / The extremal truncated moment problem / Integral Equations Operator Theory 60(2):177~200
R. Curto / 2010 / A new approach to the 2-variable subnormal completion problem / J. Math. Anal. Appl 370(1):270~283
R. Curto / 1991 / Recursiveness, positivity, and truncated moment prob-lems / Houston J. Math 17(4):603~635
R. Curto / 2008 / An analogue of the Riesz-Haviland theorem for the truncated moment problem / J. Funct. Anal 255(10):2709~2731
R. Curto / 2008 / The extremal truncated moment problem / Integral Equations Operator Theory 60(2):177~200
R. Curto / 2010 / A new approach to the 2-variable subnormal completion problem / J. Math. Anal. Appl 370(1):270~283
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