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Colloquium

Mathematics Colloquium

Date:
Time:
4:00 pm – 4:50 pm
Avery Hall Room: 115
1144 T St
Lincoln NE 68508
Additional Info: AVH
Contact:
Steve Cohn, (402) 472-7223, scohn1@math.unl.edu
Speaker: Keri Kornelson
Affiliation: University of Oklahoma
Local Host: Allan Donsig
Title: Fourier bases on fractals

Additional Public Info:

Abstract: The study of Bernoulli convolution measures dates back to the 1930’s,
yet there has been a recent resurgence in the theory prompted by the
connection between convolution measures and iterated function systems
(IFSs). The measures are supported on fractal Cantor subsets of the
real line, and exhibit their own sort of self-similarity. We will use
the IFS connection to discover Fourier bases on the L^2 Hilbert spaces
with respect to Bernoulli convolution measures.

There are some interesting phenomena that arise in this setting. We
find that some Cantor sets support Fourier bases while others do not.
In cases where a Fourier basis does exist, we can sometimes scale or
shift the Fourier frequencies by an integer to obtain another ONB. We
also discover properties of the unitary operator mapping between two
such bases. The self-similarity of the measure and the support space
can, in some cases, carry over into a self-similarity of the operator.

Refreshments will be served in 348 Avery 3:30-4pm. The talk is free and open to the public.

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This event originated in Math Colloquia.