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Seminars and Lectures

Київський математичний колоквіум

Organiser: КМТ
Location: Інститут математики НАНУ, 305, 15.00
Date Seminar
31, March 2017
15:00 Friday
The Hilbert transform intertwines a Perron-Frobenius operator
Alfonso Montes Rodriguez (University of Sevilla, Spain)

A Heisenberg uniqueness pair is a pair $(\Gamma, \Lambda)$, where $\Gamma$ is a curve and $\Lambda$ is a set in the plane $\mathbb{R}^{2}$, with the following property: any finite Borel measure $\mu$ in the plane supported on $\Gamma$, which is absolutely continuous with respect to arc length, and whose Fourier transform $\widehat{\mu}$ vanishes on $\Gamma$, must automatically be the zero measure. It will be shown how Perron–-Frobenius operators are intimately related to the Hilbert transform and to the Heisenberg uniqueness pairs associated with the hyperbola $x_{1} x_{2} = 1$.
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