All Questions

Did anyone ever consider a "function" or "distribution" $F(x)$ with the following property: its integral $\int_a^b F(x)\,dx=0$ for any finite interval $(a,b)$ but $\int_{-\infty}^\...

I want to calculate / simplify: $$\mathcal{F} (\ln(|x|)\mathcal{F(f)}(x))=\mathcal{F} (\ln(|x|)) \star f$$ where $\mathcal{F}$ is the Fourier transform ($\mathcal[f](\xi)=\int_{\mathbb R}f(x)e^{ix\...

I was thinking a bit about distribution theory the last weeks and stumbled across the following question: There are two natural locally convex topologies on the space of smooth functions of moderate ...

This should really be well-known, but I was not able to find a definite answer to this question: Is the Fourier transform of a bounded function always a borel measure (i.e. an order 0 distribution)? ...

I am attempting to look at some Liouville type theorems via a Fourier analysis approach and after looking at a baby problem I seem to be very confused. I assume this doesn't count as a research ...