论文标题
Gelfand-Shilov空间的傅立叶特征和非平地，并应用于Toeplitz运营商
Fourier characterizations and non-triviality of Gelfand-Shilov spaces, with applications to Toeplitz operators
论文作者
论文摘要
我们检查了Gelfand-Shilov空间的属性$ S_S $，$ S^σ$，$ S^σ_s$，$σ_s$，$σ^σ$和$σ^σ_s$。这些是光滑函数的空间，其中功能或其傅立叶变换允许亚指数衰减。可以确定$σ^σ_s$在且仅当$ s+σ> 1 $时是不平凡的。我们发现对功能的增长估计值及其在单参数空间中的傅立叶变换，并根据这些空间及其双重的短期傅立叶变换的估计来获得特征。此外，我们确定了托管操作员符号的条件，在该符号下，操作员在单参数空间上连续的条件。
We examine properties of Gelfand-Shilov spaces $S_s$, $S^σ$, $S^σ_s$, $Σ_s$, $Σ^σ$ and $Σ^σ_s$. These are spaces of smooth functions where the functions or their Fourier transforms admit sub-exponential decay. It is determined that $Σ^σ_s$ is nontrivial if and only if $s+ σ > 1$. We find growth estimates on functions and their Fourier transforms in the one-parameter spaces, and we obtain characterizations in terms of estimates of short-time Fourier transforms for these spaces and their duals. Additionally, we determine conditions on the symbols of Toeplitz operators under which the operators are continuous on one-parameter spaces.
