Zero integrals on circles and characterizations of harmonic and analytic functions

Globevnik, Josip

doi:10.1090/S0002-9947-1990-0958892-1

Zero integrals on circles and characterizations of harmonic and analytic functions
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Trans. Amer. Math. Soc. 317 (1990), 313-330 Request permission

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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Cours d’analyse mathématique

Sigurdur Helgason, The Radon transform, 2nd ed., Progress in Mathematics, vol. 5, Birkhäuser Boston, Inc., Boston, MA, 1999. MR 1723736, DOI 10.1007/978-1-4757-1463-0
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Sur l’equation de Volterra

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Integral geometry and inverse problems for hyperbolic equations

Théorie générale des fonctionelles