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The Set of Continuous Functions with the Everywhere Convergent Fourier Series

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. 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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.2307/2000906DOIUNSPECIFIED
http://www.jstor.org/stable/info/2000906PublisherUNSPECIFIED
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.
Funders:
Funding AgencyGrant Number
NSFDMS-8416349
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR0887506
Issue or Number:1
Classification Code:1980 Mathematics Subject Classification (1985 Revision) Primary 03E15, 26A21, 42A20
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:03 Oct 2019 04:59

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