论文标题
$ \ MATHCAL {S}_Ω（\ Mathbb {r}^n）$上的储备金
Convolutors on $\mathcal{S}_ω(\mathbb{R}^N)$
论文作者
论文摘要
在本文中，我们继续研究空间$ \ MATHCAL {O} _ {M，ω}（\ Mathbb {r}^n）$和$ \ Mathcal {o} _ {c，ω}（\ Mathbb {r}^n）$。我们确定了此类空间的新表示形式，并为其双重空间提供了一些结构定理。此外，我们表明$ \ Mathcal {o}'_ {C，ω}（\ Mathbb {r}^n）$是空间储备的空间$ \ MATHCAL {s}_Ω（\ Mathbb {r Mathbb {r}^n）$ be-um-ultrAdiftrys sensellys sensillys sensellys sensellys sensellys sensillys sensillys sensillys sensillys sensellys sensellys sensillys sensillys sensellys synections（ Braun，Meise和Taylor）及其双空间$ \ MATHCAL {S}'_Ω（\ Mathbb {r}^n）$。我们还确定，傅立叶变换是从$ \ Mathcal {o}'_ {c，ω}（\ Mathbb {r}^n）$到$ \ Mathcal {o} _ {o} _ {m，ω}（\ MathBB {\ MathBB {r}^n）$的同构。特别是，当以前的空间赋予由$ \ Mathcal {l} _B（\ Mathcal {s}_Ω（\ Mathbb {r}^n））诱导的强大操作员LC-TOPOLOGE时，我们证明这种同构是拓扑。
In this paper we continue the study of the spaces $\mathcal{O}_{M,ω}(\mathbb{R}^N)$ and $\mathcal{O}_{C,ω}(\mathbb{R}^N)$ undertaken in [1]. We determine new representations of such spaces and we give some structure theorems for their dual spaces. Furthermore, we show that $\mathcal{O}'_{C,ω}(\mathbb{R}^N)$ is the space of convolutors of the space $\mathcal{S}_ω(\mathbb{R}^N)$ of the $ω$-ultradifferentiable rapidly decreasing functions of Beurling type (in the sense of Braun, Meise and Taylor) and of its dual space $\mathcal{S}'_ω(\mathbb{R}^N)$. We also establish that the Fourier transform is an isomorphism from $\mathcal{O}'_{C,ω}(\mathbb{R}^N)$ onto $\mathcal{O}_{M,ω}(\mathbb{R}^N)$. In particular, we prove that this isomorphism is topological when the former space is endowed with the strong operator lc-topology induced by $\mathcal{L}_b(\mathcal{S}_ω(\mathbb{R}^N))$ and the last space is endowed with its natural lc-topology.
