A note on characteristic functions and their extensions
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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 that does not contain the origin, there exists a characteristic function g coinciding with f on I but not on the whole ℝ?
Keywordscharacteristic function density function entire function of exponential type probability measure
MSC30D15 42A38 42A82 60E10
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- 5.B.Ya. Levin, Lectures on Entire Functions, Transl. Math. Monogr., Vol. 150, AMS, Providence, RI, 1996.Google Scholar