Journal article
SCALING BY 5 ON A 1/4-CANTOR MEASURE
The Rocky Mountain journal of mathematics, Vol.44(6), pp.1881-1901
01/01/2014
DOI: 10.1216/RMJ-2014-44-6-1881
Abstract
Each Cantor measure mu with scaling factor 1/2n has at least one associated orthonormal basis of exponential functions (ONB) for L-2(mu). In the particular case where the scaling constant for the Cantor measure is 1/4 and two specific ONBs are selected for L-2(mu(1/4)), there is a unitary operator U defined by mapping one ONB to the other. This paper focuses on the case in which one ONB Gamma is the original Jorgensen-Pedersen ONB for the Cantor measure mu(1/4) and the other ONB is 5 Gamma. The main theorem of the paper states that the corresponding operator U is ergodic in the sense that only the constant functions are fixed by U.
Details
- Title: Subtitle
- SCALING BY 5 ON A 1/4-CANTOR MEASURE
- Creators
- Palle E. T Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USAKeri A Kornelson - Univ Oklahoma, Dept Math, Norman, OK 73019 USAKaren L Shuman - Grinnell Coll, Dept Math & Stat, Grinnell, IA 50112 USA
- Resource Type
- Journal article
- Publication Details
- The Rocky Mountain journal of mathematics, Vol.44(6), pp.1881-1901
- Publisher
- ROCKY MT MATH CONSORTIUM
- DOI
- 10.1216/RMJ-2014-44-6-1881
- ISSN
- 0035-7596
- eISSN
- 1945-3795
- Number of pages
- 21
- Grant note
- DMS-0701164 / NSF; National Science Foundation (NSF) Grinnell College Committee
- Language
- English
- Date published
- 01/01/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9984240774602771
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