论文标题
关于谐波振荡器的高斯衰减率和相关傅立叶不确定性原理的等效率
On Gaussian decay rates of harmonic oscillators and equivalences of related Fourier uncertainty principles
论文作者
论文摘要
我们在Vemuri关于谐波振荡器的最佳高斯衰减的问题上取得了进展，证明了原始的猜想至时代的算术发展。所使用的技术是根据FreeSchrödinger方程，在Cowling，Accauriaza，Kenig，Ponce和Vega的工作中开发的机械的合适翻译，以及平均衰减与点型衰减有关的引理。 这种引理在不确定性原则的等价方面产生了更多的后果。补充这种结果，我们为某些拉普拉斯变换引起的特定类别提供了端点结果，无论是衰减引理和Vemuri猜想的其余案例，都揭示了完整的端点问题。
We make progress on a question by Vemuri on the optimal Gaussian decay of harmonic oscillators, proving the original conjecture up to an arithmetic progression of times. The techniques used are a suitable translation of the problem at hand in terms of the free Schrödinger equation, the machinery developed in the work of Cowling, Escauriaza, Kenig, Ponce and Vega , and a lemma which relates decay on average to pointwise decay. Such a lemma produces many more consequences in terms of equivalences of uncertainty principles. Complementing such results, we provide endpoint results in particular classes induced by certain Laplace transforms, both to the decay Lemma and to the remaining cases of Vemuri's conjecture, shedding light on the full endpoint question.
