Zero integrals on circles and characterizations of harmonic and analytic functions-Reference-Cited by-同舟云学术

Zero integrals on circles and characterizations of harmonic and analytic functions

Published:1990 Issue:1 Volume:317 Page:313-330
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Globevnik Josip

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1990-317-01/S0002-9947-1990-0958892-1/S0002-9947-1990-0958892-1.pdf

Reference12 articles.

1. A Radon transform on spheres through the origin in 𝑅ⁿ and applications to the Darboux equation;Cormack, A. M.;Trans. Amer. Math. Soc.,1980

2. Analyticity on rotation invariant families of curves;Globevnik, Josip;Trans. Amer. Math. Soc.,1983

3. Testing analyticity on rotation invariant families of curves;Globevnik, Josip;Trans. Amer. Math. Soc.,1988

4. A characterization of harmonic functions;Globevnik, Josip;Nederl. Akad. Wetensch. Indag. Math.,1988

Cited by 12 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Analogs of the Globevnik problem on Riemannian two-point homogeneous spaces;Mathematical Notes;2017-03

2. One Problem Connected with the Helgason Support Problem;Ukrainian Mathematical Journal;2016-02

3. Microlocal Analysis of Elliptical Radon Transforms with Foci on a Line;The Mathematical Legacy of Leon Ehrenpreis;2012

4. Analogues of the problem of analytic continuation from circles for some differential equations;Doklady Mathematics;2010-08

5. Analyticity on circles for rational and real-analytic functions of two real variables;Journal d'Analyse Mathématique;2003-12