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2020 Krein condition and the Hilbert transform
Marcos López-García
Electron. Commun. Probab. 25: 1-7 (2020). DOI: 10.1214/20-ECP351

Abstract

The Krein condition has 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.

Citation

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Marcos López-García. "Krein condition and the Hilbert transform." Electron. Commun. Probab. 25 1 - 7, 2020. https://doi.org/10.1214/20-ECP351

Information

Received: 14 July 2020; Accepted: 18 September 2020; Published: 2020
First available in Project Euclid: 1 October 2020

MathSciNet: MR4158231
Digital Object Identifier: 10.1214/20-ECP351

Subjects:
Primary: 44A15, 44A60, 62E10

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