A Non-Constant Continuous Function on the Plane Whose Integral on Every Line Is Zero

DOI10.2307/2975138zbMath0838.30035OpenAlexW4232459647MaRDI QIDQ4838594

David H. Armitage

Publication date: 12 July 1995

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2975138

zbMATH Keywords

non-integrable entire functionsZalcman type example

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Integration of real functions of several variables: length, area, volume (26B15) Entire and meromorphic functions of one complex variable, and related topics (30D99)

Related Items (8)

Radon transforms and Gegenbauer-Chebyshev integrals. I ⋮ Small entire functions with extremely fast growth ⋮ GLOBAL UNIQUENESS FOR THE RADON TRANSFORM ⋮ Null spaces of Radon transforms ⋮ Tensor tomography on Cartan–Hadamard manifolds ⋮ Small entire functions with infinite growth index ⋮ Radon-John transforms and spherical harmonics ⋮ Linear subsets of nonlinear sets in topological vector spaces

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