发表机构
University of Novi Sad; Technical Faculty ”Mihajlo Pupin”, University of Novi Sad; Faculty of Sciences, University of Novi Sad（诺维萨德大学; 诺维萨德大学米哈伊洛·皮平技术学院; 诺维萨德大学理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究扩展Gevrey类中的插值问题，证明在适当增长条件下，沿发散导数阶序列的估计可推广至所有阶，并量化参数变化，同时建立扩展Gelfand--Shilov空间的插值原理。
AI 中文摘要
我们研究了由序列$M_n^{\tau,\sigma}=n^{\tau n^\sigma}$（$n\in\mathbb N$，$\tau>0$，$\sigma>1$）定义的扩展Gevrey类中的插值问题。我们证明，在导数阶发散序列满足适当增长条件的情况下，仅沿该序列施加的扩展Gevrey型估计蕴含所有导数阶的相应估计。特别地，我们显式量化了所得估计中参数的变化。为此，我们首先建立了扩展Gevrey类两种定义之间的等价性，一种涉及超几何因子$h^{n^\sigma}$，另一种则省略该因子。随后，我们建立了扩展Gelfand--Shilov空间的相应插值原理，包括对称刻画以及用定义序列的关联函数表述的形式。
英文摘要
We study an interpolation problem in extended Gevrey classes defined by the sequences $M_n^{τ,σ}=n^{τn^σ}$, $n\in\mathbb N$, $τ>0$, $σ>1$. We show that, under a suitable growth condition on a divergent sequence of derivative orders, estimates of extended Gevrey type imposed only along this sequence imply corresponding estimates for all derivative orders. In particular, we explicitly quantify the change of the parameters in the resulting estimates. To this end, we first establish an equivalence between two definitions of the extended Gevrey classes, one involving the supergeometric factor $h^{n^σ}$ and another in which this factor is omitted. We then establish a corresponding interpolation principle for extended Gelfand--Shilov spaces, including a symmetric characterization and a formulation in terms of the associated function of the defining sequence.
