Factorization properties of smooth functions and vectors

Abstract: Given a module $\mathcal{M}$ over a non-unital algebra $\mathcal{A}$, we say that $\mathcal{M}$ has the weak factorization property if $\mathcal{M}= \mathrm{span} \{\mathcal{A} \cdot \mathcal{M}\}$, while it has the strong factorization property if $\mathcal{M}= \mathcal{A} \cdot \mathcal{M}$. In this talk we shall review old and recent results about strong and weak factorizations of smooth functions and smooth vectors of Lie group representations. We shall also discuss open problems and current lines of research.

classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory

Audience: researchers in the topic

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