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
- Published Version
See Usage Policy.
Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20130524-113257744
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.
|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.|
|Other Numbering System:|
|Classification Code:||1980 Mathematics Subject Classification (1985 Revision). Primary 42A63, 43A46|
|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.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||24 May 2013 21:00|
|Last Modified:||24 May 2013 21:00|
Repository Staff Only: item control page