Published April 1989
| Published
Journal Article
Open
Hausdorff Measures and Sets of Uniqueness for Trigonometric Series
- Creators
- Dougherty, R.
- Kechris, A. S.
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.
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.Attached Files
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Additional details
- Eprint ID
- 38667
- Resolver ID
- CaltechAUTHORS:20130524-113257744
- DMS-8718847
- NSF
- Created
-
2013-05-24Created from EPrint's datestamp field
- Updated
-
2021-11-09Created from EPrint's last_modified field
- Other Numbering System Name
- MathSciNet Review
- Other Numbering System Identifier
- MR0946633