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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The $ L^p$ norm of sums of translates of a function


Author: Kanter Marek
Journal: Trans. Amer. Math. Soc. 179 (1973), 35-47
MSC: Primary 43A15
DOI: https://doi.org/10.1090/S0002-9947-1973-0361617-4
MathSciNet review: 0361617
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Abstract: For p not an even integer, $ p > 0$, we prove that knowledge of the $ {L^p}$ norm of all linear combinations of translates of a real valued function in $ {L^p}(R)$ determines the function up to translation and multiplication by $ \pm 1$.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0361617-4
Keywords: Fourier transform, $ {L^p}$ norm of translates, measures on spheres
Article copyright: © Copyright 1973 American Mathematical Society