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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Sets of uniqueness on the $ 2$-torus

Author: Victor L. Shapiro
Journal: Trans. Amer. Math. Soc. 165 (1972), 127-147
MSC: Primary 42A92; Secondary 43A55
MathSciNet review: 0308684
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Abstract: $ {H^{(J)}}$-sets are defined on the 2-torus and the following results are established: (1) $ {H^{(J)}}$-sets are sets of uniqueness both for Abel summability and circular convergence of double trigonometric series; (2) a countable union of closed sets of uniqueness of type (A) (i.e., Abel summability) is also a set of uniqueness of type (A).

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Keywords: Double trigonometric series, formal multiplication of trigonometric series, sets of uniqueness, torus, localization, normal sequence, Abel summability, Bochner-Riesz summability, Riemannian theory, Baire category
Article copyright: © Copyright 1972 American Mathematical Society