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- W4287704703 abstract "In measure theory several results are known how measure spaces are transformed into each other. But since moment functionals are represented by a measure we investigate in this study the effects and implications of these measure transformations to moment funcationals. We gain characterizations of moments functionals. Among other things we show that for a compact and path connected set $Ksubsetmathbb{R}^n$ there exists a measurable function $g:Kto [0,1]$ such that any linear functional $L:mathbb{R}[x_1,dots,x_n]tomathbb{R}$ is a $K$-moment functional if and only if it has a continuous extension to some $overline{L}:mathbb{R}[x_1,dots,x_n]+mathbb{R}[g]tomathbb{R}$ such that $tilde{L}:mathbb{R}[t]tomathbb{R}$ defined by $tilde{L}(t^d) := overline{L}(g^d)$ for all $dinmathbb{N}_0$ is a $[0,1]$-moment functional (Hausdorff moment problem). Additionally, there exists a continuous function $f:[0,1]to K$ independent on $L$ such that the representing measure $tilde{mu}$ of $tilde{L}$ provides the representing measure $tilde{mu}circ f^{-1}$ of $L$. We also show that every moment functional $L:mathcal{V}tomathbb{R}$ is represented by $lambdacirc f^{-1}$ for some measurable function $f:[0,1]tomathbb{R}^n$ where $lambda$ is the Lebesgue on $[0,1]$." @default.
- W4287704703 created "2022-07-26" @default.
- W4287704703 creator A5010485476 @default.
- W4287704703 date "2020-07-27" @default.
- W4287704703 modified "2023-09-26" @default.
- W4287704703 title "Transformations of Moment Functionals" @default.
- W4287704703 doi "https://doi.org/10.48550/arxiv.2007.13347" @default.
- W4287704703 hasPublicationYear "2020" @default.
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