A note on uniqueness of extension for characteristic functions

2020/09/09 by Саулюс Норвидас, Norvidas, Saulius
Mathematics · Computer Science · #Mathematical Analysis and Transform Methods #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2009.04497

Abstract

Let f:R→ C be the characteristic function of a probability measure. We study the following question: Is it true that for any closed interval I on R, which does not contain the origin, there exists a characteristic function g such that g coincides with f on I but g \not≡ f on R?

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