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- W1567843224 abstract "Given real numbers $beta equiv beta ^{left ( 4right ) }colon beta _{00}$, $beta _{10}$, $beta _{01}$, $beta _{20}$, $beta _{11}$, $beta _{02}$, $beta _{30}$, $beta _{21}$, $beta _{12}$, $beta _{03}$, $beta _{40}$, $beta _{31}$, $beta _{22}$, $beta _{13}$, $beta _{04}$, with $beta _{00} >0$, the quartic real moment problem for $beta$ entails finding conditions for the existence of a positive Borel measure $mu$, supported in $mathbb {R}^2$, such that $beta _{ij}=int s^{i}t^{j} dmu ;;(0leq i+jleq 4)$. Let $mathcal {M}(2)$ be the $6 times 6$ moment matrix for $beta ^{(4)}$, given by $mathcal {M}(2)_{mathbf {i}, mathbf {j}}:=beta _{mathbf {i}+mathbf {j}}$, where $mathbf {i},mathbf {j} in mathbb {Z}^2_+$ and $left |mathbf {i}right |,left |mathbf {j}right |le 2$. In this note we find concrete representing measures for $beta ^{(4)}$ when $mathcal {M}(2)$ is nonsingular; moreover, we prove that it is possible to ensure that one such representing measure is $6$-atomic." @default.
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- W1567843224 date "2015-06-30" @default.
- W1567843224 modified "2023-10-14" @default.
- W1567843224 title "Concrete solution to the nonsingular quartic binary moment problem" @default.
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- W1567843224 doi "https://doi.org/10.1090/proc/12698" @default.
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