Abstract
IfX is a locally compact abelian group, μ a probability measure onX and\(\hat \mu \) its Fourier transform, the mapping μ→|\(\hat \mu \)| is obviously not injective. The aim of this article is to find conditions under which the identification of μ given |\(\hat \mu \)| is possible up to a shift and a central symmetry.
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Research partially supported by the Swiss National Science Foundation.
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Carnal, H., Fel'dman, G.M. Phase retrieval for probability measures on abelian groups. J Theor Probab 8, 717–725 (1995). https://doi.org/10.1007/BF02218053
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DOI: https://doi.org/10.1007/BF02218053