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Does convergence of tempered distributions implies convergence in $\mathcal{S}(\mathbb{R}^4,\mathbb{R})/\mathcal{S}_{0}$?

We can define the following symmetric semi-definite positive bi-linear form on $\mathcal{S}(\mathbb{R}^{4},\mathbb{R})$ with values in $\mathbb{C}$, \begin{equation}\label{prodintespaciales} (h_{...
Gabriel Palau's user avatar
6 votes
0 answers
159 views

Fourier transformation of a distribution

We have no idea how to tackle the following Fourier transformation of a distribution: $$ \lim_{\epsilon\to0^+}\int_{-\infty}^{\infty}\mathrm{d} t\int_{\mathbb{R}^{d-1}} \mathrm{d}^{d-1}\vec{r} e^{-\...
Y.Okuyama's user avatar
  • 373
4 votes
2 answers
405 views

Fourier transform of a Lorentz invariant generalized function

Consider on $\mathbb{R}^{n+1}$ the indefinite quadratic form defining the Minkowski metric $$B(p)=(p^0)^2-(p^1)^2-\dots-(p^n)^2.$$ Let $\mu$ be a generalized function on $\mathbb{R}^{n+1}$ which is ...
asv's user avatar
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