Robert Xu Yang, Department of Pure Mathematics, University of Waterloo
"Interpolation Sets in Harmonic Analysis"
Many classical harmonic analysis results are based on 'Lacunary or Hadamard sets'. Weierstrass used Hadamard sequences to build the first example of nowhere differentiable continuous function. Hadamard sets also inspired the classical Hadamard gap theorem and the Riesz product measure, which is an example of a continuous measure whose Fourier coefficients do not vanish at infinity.
Hadamard sets have very good interpolation properties and these have motivated the study of interpolation sets in more general settings. In this talk we focus on one type of interpolation sets called Sidon sets. A Sidon set E is a set with the property that we can interpolate every bounded function on E by a Fourier transform of a measure. We will show many equivalent descriptions of Sidon sets and will discuss the decomposition of Sidon sets into even more special sets.
MC 5417