论文标题
凯林状况和希尔伯特变革
Krein condition and the Hilbert transform
论文作者
论文摘要
凯林条件已被用作定性结果，以表明某种密度的M-差异性。在这项工作中，我们将希尔伯特转型理论的结果用于构建密度的家族，具有与有限对数积分的密度$ f $相同的有限矩序列。实际上，我们的方法显式地为$ f $的中心提供了stieltjes课程，涉及$ \ lnf。$的希尔伯特变换的扰动，我们考虑整个真实线或正线支持的密度。
Krein condition have been used as a qualitative result to show the M-indeterminacy of some kind of densities. In this work we use results from the theory of the Hilbert transform to construct families of densities having all the same finite moment sequence as a density $f$ with finite logarithmic integral. Actually, our approach explicitly gives Stieltjes classes with center at $f$ and perturbations involving the Hilbert transform of $\ln f.$ We consider densities supported on the whole real line or the positive half line.
