Fourier transform and rigidity of certain distributions

Details Fourier transform and rigidity of certain distributions Fourier transform and rigidity of certain distributions

2010-10-12

arxiv.org/abs/1010.2342v2

Mathematics

Functional Analysis

9 pages

Scientific paper

Let $E$ be a finite dimensional vector space over a local field, and $F$ be its dual. For a closed subset $X$ of $E$, and $Y$ of $F$, consider the space $D^{-\xi}(E;X,Y)$ of tempered distributions on $E$ whose support are contained in $X$ and support of whose Fourier transform are contained in $Y$. We show that $D^{-\xi}(E;X,Y)$ possesses a certain rigidity property, for $X$, $Y$ which are some finite unions of affine subspaces.

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