Tiling by translates of a function

Abstract: I will discuss tilings of the real line by translates of a function $f$, that is, systems $\{f(x - \lambda), \lambda \in \Lambda\}$ of translates of $f$ that form a partition of unity. Which functions $f$ can tile by translations, and what can be the structure of the translation set $\Lambda$? I will survey the subject and present some recent results.

classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory

Audience: researchers in the topic

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