Speaker
De-Jun Feng, Chinese University of Hong Kong
Abstract
Let \(\mu\) be the self-affine measure associated with a homogeneous affine IFS \(\Phi\) on \(\mathbb{R}^d\) and a strictly positive probability vector. Assume that the attractor of \(\Phi\) is not contained in any affine hyperplane. We show that \(\mu\) is non-Rajchman (i.e., its Fourier transform does not vanish at infinity) if and only if one of the following algebraic conditions holds: (i) \(\Phi\) is a generalized Pisot IFS of type~I; or (ii) the affine system has a singular integral factor. I will explain these two conditions. This talk is based on joint work with Tianhan Yi.