Amlan Banaji [WS1]: Fourier decay from L^2-flattening

Speaker
Amlan Banaji, University of Jyväskylä

Abstract
If a measure mu on R^d does not locally concentrate too much around affine hyperplanes, then mu is known to be `L^2-flattening.’ This means that its L^2 dimension increases under iterated self-convolutions, which can be shown to imply that its Fourier transform decays outside a very sparse set of exceptional frequencies. We will explain how this can be used to prove that if a conformal iterated function system satisfies natural nonlinearity conditions then the resulting self-conformal measures have polynomial Fourier decay. This talk is based on (separate) joint work with Simon Baker and Han Yu, and on work by other authors.