Uncertainty Principle for the Cantor Dyadic Group

2013/11/16 by Aleksander V. Krivoshein, Krivoshein, Aleksander V., Elena A. Lebedeva +1
Mathematics · #22B99 #42C40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:22B99 #msc:42C40

paper · pdf · doi:10.48550/arxiv.1311.4065

14 pages

arxiv created 2013/12/08 · arxiv updated 2013/12/10

Abstract

We introduce a notion of localization for dyadic functions, i.e. functions defined on the Cantor group. Localization is characterized by functional UC_d similar to the Heisenberg uncertainty constant used for real-line functions. We are looking for dyadic analogs of quantitative uncertainty principles. To justify definition we use some test functions including dyadic scaling and wavelet functions.

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