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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A Cantor-Lebesgue theorem in two dimensions


Author: Roger Cooke
Journal: Proc. Amer. Math. Soc. 30 (1971), 547-550
MSC: Primary 42.10
MathSciNet review: 0282134
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Abstract: We prove a partial extension of the classical result of Cantor and Lebesgue to two dimensions, for circular summation of trigonometric series. We assume convergence almost everywhere rather than merely on a set of positive measure. Although the theorem we prove has applications in uniqueness theorems, its purpose is to suggest what may be true in general, since the proof does not generalize to higher dimensions.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0282134-X
Keywords: Cantor-Lebesgue theorem, spherical summation, uniqueness of trigonometric series, multiple trigonometric series, lattice points in Euclidean space
Article copyright: © Copyright 1971 American Mathematical Society