Ajtai, M. and Kechris, A. S. (1987) The Set of Continuous Functions with the Everywhere Convergent Fourier Series. Transactions of the American Mathematical Society, 302 (1). pp. 207-221. ISSN 0002-9947. doi:10.2307/2000906. https://resolver.caltech.edu/CaltechAUTHORS:20130522-115611198
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Abstract
This paper deals with the descriptive set theoretic properties of the class EC of continuous functions with everywhere convergent Fourier series. It is shown that this set is a complete coanalytic set in C(T). A natural coanalytic rank function on EC is studied that assigns to each ƒ Є EC a countable ordinal number, which measures the "complexity" of the convergence of the Fourier series of ƒ. It is shown that there exist functions in EC (in fact even differentiable ones) which have arbitrarily large countable rank, so that this provides a proper hierarchy on EC with ω_1 distinct levels.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1987 American Mathematical Society. Received by the editors June 11, 1985 and, in revised form, June 20, 1986. Research partially supported by NSF Grant DMS-8416349. | |||||||||
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| Issue or Number: | 1 | |||||||||
| Classification Code: | 1980 Mathematics Subject Classification (1985 Revision) Primary 03E15, 26A21, 42A20 | |||||||||
| DOI: | 10.2307/2000906 | |||||||||
| Record Number: | CaltechAUTHORS:20130522-115611198 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130522-115611198 | |||||||||
| Official Citation: | The Set of Continuous Functions with the Everywhere Convergent Fourier Series M. Ajtai and A. S. Kechris Transactions of the American Mathematical Society , Vol. 302, No. 1 (Jul., 1987), pp. 207-221 Published by: American Mathematical Society Article Stable URL: http://www.jstor.org/stable/200090 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 38635 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 22 May 2013 20:27 | |||||||||
| Last Modified: | 09 Nov 2021 23:38 |
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