论文标题
加权$（plb）$ - 超放映性功能和乘数空间的空间
Weighted $(PLB)$-spaces of ultradifferentiable functions and multiplier spaces
论文作者
论文摘要
我们研究了通过重量功能（从Braun，Meise和Taylor的意义上）和权重系统定义的超平整功能的加权$（PLB）$ - 超平变功能的空间。我们表征当此类空间在定义重量系统方面是超生产的何时。这概括了Grothendieck的经典结果，即缓慢增加平滑函数的空间$ \ Mathcal {O} _m $在超放置函数的背景下是超生产的。此外，我们确定了Gelfand-Shilov空间的乘数，并通过上述结果来表征此类空间是超生产的。特别是，我们表明，傅立叶超生气功能的乘数空间是超生产学的，而傅立叶高功能的空间之一不是。
We study weighted $(PLB)$-spaces of ultradifferentiable functions defined via a weight function (in the sense of Braun, Meise and Taylor) and a weight system. We characterize when such spaces are ultrabornological in terms of the defining weight system. This generalizes Grothendieck's classical result that the space $\mathcal{O}_M$ of slowly increasing smooth functions is ultrabornological to the context of ultradifferentiable functions. Furthermore, we determine the multiplier spaces of Gelfand-Shilov spaces and, by using the above result, characterize when such spaces are ultrabornological. In particular, we show that the multiplier space of the space of Fourier ultrahyperfunctions is ultrabornological, whereas the one of the space of Fourier hyperfunctions is not.
