Sopra la trasformata di Hankel distribuzionale

Trione, Susana Elena

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 57 (1974) no. 5, pp. 316-320

Résumé

We evaluate (formula (2,2)) the Hankel transform of the distribution $\delta_{a}^{(m)}(t)$. As a consequence of (2,2) we obtain \begin{equation*} \lim_{A \to \infty} \frac{\Omega_{n}}{(2\pi)^{n/2}} \, A^{n/2} J_{n/2}(At) = \delta,\end{equation*} where $\Omega_{n}$ designates the area of the unit sphere in $R^{n}$. We also give a direct proof of this formula, which plays a role in the theory of the spherical summability of Fourier integrals.