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Transactions of the American Mathematical Society

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

 

 

Zero integrals on circles and characterizations of harmonic and analytic functions


Author: Josip Globevnik
Journal: Trans. Amer. Math. Soc. 317 (1990), 313-330
MSC: Primary 44A05; Secondary 30E20, 31A05, 45D05
MathSciNet review: 958892
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Abstract: We determine the kernels of two circular Radon transforms of continuous functions on an annulus and use this to obtain a characterization of harmonic functions in the open unit disc which involves Poisson averages over circles computed at only one point of the disc and to obtain a version of Morera's theorem which involves only the circles which surround the origin.


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DOI: https://doi.org/10.1090/S0002-9947-1990-0958892-1
Article copyright: © Copyright 1990 American Mathematical Society