About the Nuclearity of $$\mathcal {S}_{(M_{p})}$$ and $$\mathcal {S}_{\omega }$$
About the Nuclearity of $$\mathcal {S}_{(M_{p})}$$ and $$\mathcal {S}_{\omega }$$
We use an isomorphism established by Langenbruch between some sequence spaces and weighted spaces of generalized functions to give sufficient conditions for the (Beurling type) space ${\mathcal S}_{(M_p)}$ to be nuclear. As a consequence, we obtain that for a weight function $\omega$ satisfying the mild condition: $2\omega(t)\leq \omega(Ht)+H$ for some …