IRMACS: The Interdisciplinary Colloquium - Special Session: "The Energy integral and Fourier transform"

Abstract

In the last twenty years there have been many connections discovered between fractal geometry and harmonic analysis. One such connection is a Fourier transform formula for the energy integral of a measure, a notion which is associated with a fractal dimension. In this talk we will look at applications of this formula to the Falconer distance conjecture, a continuous analogue of the Erdos distance conjecture, and to the uncertainty principle in harmonic analysis, a general philosophy that says we can