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Analysis Seminar with Bartosz Malman, Mälardalen University

Tid: 2023-11-21 13:15 till 14:15 Seminarium

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

In Fourier analysis, there is variety of statements which postulate that a function 𝑓 and its Fourier transform ℱ𝑓 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 ℝ, and largeness will be interpreted in terms of the existence of a spectral clump for 𝑓: an interval on which ℱ𝑓 is large enough to have an integrable logarithm.

Om händelsen
Tid: 2023-11-21 13:15 till 14:15


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Sidansvarig: webbansvarig@math.lu.se | 2017-05-23