Abstract
We study the general moment problem for measures on the real line, with polynomials replaced by more general spaces of entire functions. As a particular case, we describe measures that are uniquely determined by a restriction of their Fourier transform to a finite interval. We apply our results to prove an extension of a theorem by Eremenko and Novikov on the frequency of oscillations of measures with a spectral gap (high-pass signals) near infinity.
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Acknowledgments
We are grateful to A. Eremenko and M. Sodin who brought the problem on oscillations of Fourier integrals to our attention.
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M. Mitkovski’s research is supported in part by National Science Foundation DMS grant # 1101251. A. Poltoratski’s research is supported in part by National Science Foundation DMS grant # 1101278.
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Mitkovski, M., Poltoratski, A. On the determinacy problem for measures. Invent. math. 202, 1241–1267 (2015). https://doi.org/10.1007/s00222-015-0588-6
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DOI: https://doi.org/10.1007/s00222-015-0588-6