论文标题
圆圈上移动的谐波振荡器和低纤维化拉普拉斯式
The shifted harmonic oscillator and the hypoelliptic Laplacian on the circle
论文作者
论文摘要
我们研究了该半群的低纤维化拉普拉斯人在圆圈上产生的半群和最大界面的全态扩展。我们将正交分解为具有复杂移动的谐波振荡器，我们描述了该扩展的域，并表明半平面中的界限对应于特征函数中半群的扩展的绝对收敛。这取决于光谱投影的新型积分公式，该公式也为大参数制度中的Laguerre多项式提供了渐近性。
We study the semigroup generated by the hypoelliptic Laplacian on the circle and the maximal bounded holomorphic extension of this semigroup. Using an orthogonal decomposition into harmonic oscillators with complex shifts, we describe the domain of this extension and we show that boundedness in a half-plane corresponds to absolute convergence of the expansion of the semigroup in eigenfunctions. This relies on a novel integral formula for the spectral projections which also gives asymptotics for Laguerre polynomials in a large-parameter regime.
