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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniqueness for multiple trigonometric and Walsh series with convergent rearranged square partial sums


Authors: J. Marshall Ash and Sh. T. Tetunashvili
Journal: Proc. Amer. Math. Soc. 134 (2006), 1681-1686
MSC (2000): Primary 42B99, 42B05, 42C20; Secondary 42C10, 42A63
Published electronically: December 2, 2005
MathSciNet review: 2204280
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Abstract | References | Similar Articles | Additional Information

Abstract: If at each point of a set of positive Lebesgue measure every rearrangement of a multiple trigonometric series square converges to a finite value, then that series is the Fourier series of a function to which it converges uniformly. If there is at least one point at which every rearrangement of a multiple Walsh series square converges to a finite value, then that series is the Walsh-Fourier series of a function to which it converges uniformly.


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Additional Information

J. Marshall Ash
Affiliation: Department of Mathematical Sciences, DePaul University, Chicago, Illinois 60614-3504
Email: mash@math.depaul.edu

Sh. T. Tetunashvili
Affiliation: Department of Mathematics, Georgian Technical University, Kostava str. 77, 0175 Tbilisi, Republic of Georgia
Email: stetun@hotmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08225-0
PII: S 0002-9939(05)08225-0
Keywords: Uniqueness, multiple trigonometric series, multiple Walsh series, rearrangements
Received by editor(s): January 4, 2005
Published electronically: December 2, 2005
Additional Notes: This research was partially supported by NSF grant DMS 9707011 and a grant from the Faculty and Development Program of the College of Liberal Arts and Sciences, DePaul University.
Communicated by: Andreas Seeger
Article copyright: © Copyright 2005 American Mathematical Society