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- W2316303012 abstract "for every (doubly infinite) line l, where s denotes length measure, then f must be identically zero. This has been known for many years (see [5] for references), but only comparatively recently was it shown that this result fails in the absence of the global integrability condition. In fact, Zalcman [S; pp. 243-244], using a theorem of Arakelian [1; p. 1189] concerning tangential holomorphic approximation on unbounded sets, constructed a non-constant entire function t satisfying (1) on every line 1. The purpose of this note is to give a construction, similar to Zalcman's, but using only elementary complex analysis. As a bonus all the derivatives of the function we produce also have vanishing integrals on all lines. The main idea is to construct a non-constant entire function g whose derivatives satisfy" @default.
- W2316303012 created "2016-06-24" @default.
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- W2316303012 date "1994-11-01" @default.
- W2316303012 modified "2023-09-28" @default.
- W2316303012 title "A Non-Constant Continuous Function on the Plane Whose Integral on Every Line Is Zero" @default.
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- W2316303012 doi "https://doi.org/10.1080/00029890.1994.11997043" @default.
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