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arXiv · 2012.07258

Any multi-index sequence has an interpolating measure

Hayoung Choi·Seonguk Yoo
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Abstract

R. P. Boas showed that any single-index sequence $\left\{ \beta_i \right\}_{i=0}^\infty$ of real numbers can be represented as $\beta_i =\int_0^\infty x^i \, d\mu$ ($i=0,1,2,\ldots$), where $\mu$ is a signed measure. As Boas said his observation seemed to be quite unexpected; however, it is even possible to extend the result to any multi-index sequence of real numbers. In addition, we can also prove that any multi-index finite sequence admits a measure of a similar type.

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Hayoung Choi, Seonguk Yoo. 2020-12-14. Any multi-index sequence has an interpolating measure. https://arxiv.org/abs/2012.07258

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