Some remarks on the Pompeiu problem for groups

Authors:
David Scott and Alladi Sitaram

Journal:
Proc. Amer. Math. Soc. **104** (1988), 1261-1266

MSC:
Primary 43A60; Secondary 22E30, 43A80

DOI:
https://doi.org/10.1090/S0002-9939-1988-0931747-0

MathSciNet review:
931747

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Abstract: A Borel set in a topological group is said to be a -set for the space of integrable functions on if the zero function is the only integrable function whose integral over all left and right translates of by elements of is zero. For a "sufficiently nice" group and a Borel set of finite Haar measure a certain condition on the Fourier transform of a function related to is shown to be a sufficient condition for to be a -set. This condition is then applied to several classes of groups including certain compact groups, certain semisimple Lie groups, the Heisenberg groups and the Euclidean motion group of the plane.

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0931747-0

Article copyright:
© Copyright 1988
American Mathematical Society