Session S13 - Harmonic Analysis, Fractal Geometry, and Applications

Tuesday, July 20, 17:45 ~ 18:15 UTC-3

Some topics in harmonic analysis over locally compact abelian groups

Emily King

Colorado State University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Many results in harmonic analysis over Euclidean space rely on the existence of full rank lattices in $\mathbb{R}^d$ to generate translation groups. Thus, it is not always possible to simply port over proofs from harmonic analysis over $\mathbb{R}^d$ to harmonic analysis over locally compact abelian groups without lattices, like vector spaces over the $p$-adic numbers $\mathbb{Q}_p^d$. In this talk, some results about wavelet and Gabor systems over such groups with connections to fractal geometry will be presented.

Joint work with Victoria Paternostro (Universidad de Buenos Aires, Argentina) and Maria Skopina (Saint Petersburg State University, Russia).

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