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Hausdorff Measures and Sets of Uniqueness for Trigonometric Series

Dougherty, R. and Kechris, A. S. (1989) Hausdorff Measures and Sets of Uniqueness for Trigonometric Series. Proceedings of the American Mathematical Society, 105 (4). pp. 894-897. ISSN 0002-9939. http://resolver.caltech.edu/CaltechAUTHORS:20130524-113257744

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Abstract

We characterize the closed sets E in the unit circle T which have the property that, for some nondecreasing h: (0, ∞) →(0, ∞) with h(0+) = 0, all the Hausdorff h-measure 0 closed sets F ⊆ E are sets of uniqueness (for trigonometric series). In conjunction with Körner's result on the existence of Helson sets of multiplicity, this implies the existence of closed sets of multiplicity (M-sets) within which Hausdorff h-measure 0 implies uniqueness, for some h. This is contrasted with the case of closed sets of strict multiplicity (M_0-sets), where results of Ivashev-Musatov and Kaufman establish the opposite.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.2307/2047049DOIUNSPECIFIED
http://www.ams.org/journals/proc/1989-105-04/S0002-9939-1989-0946633-0/home.htmlPublisherUNSPECIFIED
http://www.jstor.org/stable/2047049PublisherUNSPECIFIED
Additional Information:© 1989 American Mathematical Society. Received by the editors April 21, 1988 and, in revised form, June 1, 1988. The second author was partially supported by NSF Grant DMS-8718847.
Funders:
Funding AgencyGrant Number
NSFDMS-8718847
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR0946633
Classification Code:1980 Mathematics Subject Classification (1985 Revision). Primary 42A63, 43A46
Record Number:CaltechAUTHORS:20130524-113257744
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20130524-113257744
Official Citation:Hausdorff measures and sets of uniqueness for trigonometric series R. Dougherty and A. S. Kechris. Proc. Amer. Math. Soc. 105 (1989), 894-897
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38667
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:24 May 2013 21:00
Last Modified:24 May 2013 21:00

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