Abstract
Consider the following question: Under which conditions is a probability measure (on the real line e.g.) uniquely determined (up to a shift) already by the absolute value of its Fourier transform? In other words: When is it possible to retrieve the phase (up to a constant) from the absolute value of the Fourier transform? This problem has its origin in crystallography and there exists a vast literature on it (there was even a Nobel prize given for this subject), see e.g. Carnal and Fel’dman[CF95, CF97] and the references cited there.
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This chapter is taken from [FNS97b].
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© 1999 Springer Science+Business Media Dordrecht
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Franz, U., Schott, R. (1999). Phase retrieval for probability distributions on quantum groups and braided groups. In: Stochastic Processes and Operator Calculus on Quantum Groups. Mathematics and Its Applications, vol 490. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9277-2_9
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DOI: https://doi.org/10.1007/978-94-015-9277-2_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5290-2
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