Bartosz Malman (Mälardalen University)

Title: Clumps, and spectral clumps, for functions on the real line

Abstract: In Fourier analysis, there is variety of statements which postulate that a function f and its Fourier transform \widehat{f} cannot simultaneously be too small, or that one of them has to be large if the other is small. What small or large means depends on context. The most famous such statement surely is the Fourier analytic version of Heisenberg's quantum mechanical uncertainty principle, but there is an abundance of other interpretations. In my talk, I want to review some other manifestations of the uncertainty principle, including theorems of Benedicks and Volberg, and I want to contribute a new interpretation which I recently stumbled upon. In my context, smallness will be interpreted in terms of a one-sided rapid decay condition on a function f living on the real line \mathbb{R}, and largeness will be interpreted in terms of the existence of a{spectral clump for f: an interval on which \widehat{f} is large enough to have an integrable logarithm. If time permits, I will discuss how this result finds applications in the theories of subnormal operators and de Branges-Rovnyak spaces.

Where: Laval, Alexandre-Vachon, VCH-3840 and by Zoom (see link below)

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https://ulaval.zoom.us/j/68099684137?pwd=L2hPdVprdUd3VHZBYkc1aTJFWU13dz09

Meeting ID: 680 9968 4137

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