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Cora Sadosky: Her Mathematics, Mentorship, and Professional Contributions Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Victor Shapiro and the Theory of Uniqueness for Multiple Trigonometric Series

Author : J. Marshall Ash

Published in: Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1)

Publisher: Springer International Publishing

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Abstract

In 1870, Georg Cantor proved that if a trigonometric series converges to 0 everywhere, then all its coefficients must be 0. In the twentieth century this result was extended to higher dimensional trigonometric series when the mode of convergence is taken to be spherical convergence and also when it is taken to be unrestricted rectangular convergence. We will describe the path to each result. An important part of the first path was Victor Shapiro’s seminal 1957 paper, Uniqueness of multiple trigonometric series. This paper also was an unexpected part of the second path.

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previous chapter Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey
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Metadata
Title
Victor Shapiro and the Theory of Uniqueness for Multiple Trigonometric Series
Author
J. Marshall Ash
Copyright Year
2016
Book
Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1)

Print ISBN: 978-3-319-30959-0

Electronic ISBN: 978-3-319-30961-3

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-30961-3_5

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