发表机构
Saint Petersburg State University（圣彼得堡国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了多维归一化L^1 Nikolskii常数的精确渐近性，通过构造容许函数和比较Bessel模型分别得到下界与上界，并确定了极值函数正零点的极限分布。
AI 中文摘要
我们证明了多维归一化$L^1$ Nikolskii常数\\[ \mathcal L^*(d)=\Bigl(\frac{\pi}{2}+o(1)\Bigr)2^{-d}, \quad d\to\infty \\]的精确渐近性。此外，对于每个固定维度，我们获得了极值函数$\varphi_d$的正零点的渐近性，并确定了它们在$d\to\infty$时的极限分布。下界来自一个容许函数的构造及其渐近分析。对于上界，我们将$x^{d+1}\varphi_d(x)$表示为方程$u''+V_d(x)u=0$的两个解的乘积，将该方程与Bessel模型进行比较，并分析相对典范乘积。
英文摘要
We prove the exact asymptotics of the multidimensional normalized $L^1$ Nikolskii constant \[ \mathcal L^*(d)=\Bigl(\fracπ{2}+o(1)\Bigr)2^{-d}, \quad d\to\infty. \] In addition, for each fixed dimension we obtain asymptotics for the positive zeros of the extremal function $φ_d$, and determine their limiting distribution as $d\to\infty$. The lower bound follows from the construction of an admissible function and its asymptotic analysis. For the upper bound, we represent $x^{d+1}φ_d(x)$ as the product of two solutions of the equation $u''+V_d(x)u=0$, compare this equation with a Bessel model, and analyze relative canonical products.
Comments27 pages
