IRMACS: The Interdisciplinary Colloquium - Special Session: "The Energy integral and Fourier transform"
University of Waterloo
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�t expect to control well both the time and spectral properties of an object.
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