关于谐振子逆算子的研究
偏微分方程分析
2014-06-05 v4
摘要
设 为 上谐振子逆算子的 Weyl 符号。我们证明 及其导数满足方便的 Gevrey 型和 Gelfand-Shilov 型界，并获得了 的显式表达式。在偶维情形下，我们用初等函数刻画了 。在分析中，我们利用径向对称性性质，并结合了多种技术，包括经典先验估计、对易子恒等式、幂级数和渐近展开。
引用
@article{arxiv.1306.6866,
title = {On the inverse to the harmonic oscillator},
author = {Marco Cappiello and Luigi Rodino and Joachim Toft},
journal= {arXiv preprint arXiv:1306.6866},
year = {2014}
}
备注
24 pages. In previous versions, certain parts were managed by arguments involving the Bargmann transform. These parts are now proved in other ways. The Bargmann parts are now moved to an other arxiv preprint