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- W3136175513 abstract "In this paper, we provide all possible characterisations of spectral measure on the real line in terms of its two moments. To be more precise, we prove that semispectral measure $F$ on the real line with compact support such that $T^p =int_{mathbb{R}} x^p F(d x)$ and $T^q =int_{mathbb{R}}x^q F(dx)$, $p<q$, $p$ odd and $q$ even, is spectral. Moreover we show that the set $Omega:={(p,q)in mathbb{N}^2colon p<q, p text{ odd and } q text{ even}}$ is best possible with respect to the above result, that is, if $(p,q)in mathbb{N}^2setminusOmega$ there exist a semispectral measure $F$ on the real line which is not spectral and $T^p =int_{mathbb{R}}x^p F(dx)$ and $T^q =int_{mathbb{R}}x^q F(dx)$." @default.
- W3136175513 created "2021-03-29" @default.
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- W3136175513 date "2021-03-18" @default.
- W3136175513 modified "2023-09-27" @default.
- W3136175513 title "Two moments characterization for a semispectral measure on the real line to be spectral" @default.
- W3136175513 hasPublicationYear "2021" @default.
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