Uniqueness for multiple trigonometric and Walsh series with convergent rearranged square partial sums
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- by J. Marshall Ash and Sh. T. Tetunashvili PDF
- Proc. Amer. Math. Soc. 134 (2006), 1681-1686 Request permission
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.References
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Additional Information
- J. Marshall Ash
- Affiliation: Department of Mathematical Sciences, DePaul University, Chicago, Illinois 60614-3504
- MR Author ID: 27660
- 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
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 1681-1686
- MSC (2000): Primary 42B99, 42B05, 42C20; Secondary 42C10, 42A63
- DOI: https://doi.org/10.1090/S0002-9939-05-08225-0
- MathSciNet review: 2204280