论文标题
四分之一振荡器的光谱总结性，并应用于Engel组
Spectral summability for the quartic oscillator with applications to the Engel group
论文作者
论文摘要
在本文中，我们研究了Engel组上Sublaplacian $-Δ__{G} $的光谱特性，这是步骤3的Carnot组的主要例子。我们根据频率集开发了对Engel组的傅立叶分析的新方法。这使我们能够对满足$ f的卷积内核进行良好的估计（-Δ_{g}）u = u \ star k_ {f} $，对于合适的标量函数$ f $，并通过傅立叶技术获得经典功能嵌入的证据。该分析需要在四分之一振荡器的频谱上具有总结性能，我们通过半经典技术获得，并且具有独立感兴趣。
In this article, we investigate spectral properties of the sublaplacian $-Δ_{G}$ on the Engel group, which is the main example of a Carnot group of step 3. We develop a new approach to the Fourier analysis on the Engel group in terms of a frequency set. This enables us to give fine estimates on the convolution kernel satisfying $F(-Δ_{G})u=u\star k_{F}$, for suitable scalar functions $F$, and in turn to obtain proofs of classical functional embeddings, via Fourier techniques. This analysis requires a summability property on the spectrum of the quartic oscillator, which we obtain by means of semiclassical techniques and which is of independent interest.
