论文标题
操作员的Wigner分析。第二部分：Schrödinger方程
Wigner Analysis of Operators. Part II: Schrödinger equations
论文作者
论文摘要
我们研究了所谓的广义元容器的相位浓度，其主要例子是具有界定扰动的Schrödinger方程。 为了实现此目标，我们执行了一个所谓的$ \ Mathcal {a} $ - 对先前方程式的Wigner分析，如第一部分中所示。 [14]。也就是说，经典的Wigner分布是通过考虑以符号矩阵$ \ mathcal $ \ Mathcal {a} \ in sp（2d，\ Mathbb {r}）构建的元素构造的一类时频表示来扩展的。这些表示形式的子类，与协变量符号矩阵有关，表明特别适合Schrödinger进化的时频研究。这证明了这种方程的有效性，这是由相关波形前组的发展强调的。 我们首先研究了$ \ Mathcal {a} $ - WIGNER表示的属性和我们目标所需的相关伪差操作员。这种方法为新的量化程序铺平了道路。 作为副产品，我们介绍了包含具有更一般潜力的Schrödinger方程的广义元容器的新的准代码，并扩展了先前的作品中所包含的结果[8,9]。
We study the phase-space concentration of the so-called generalized metaplectic operators whose main examples are Schrödinger equations with bounded perturbations. To reach this goal, we perform a so-called $\mathcal{A}$-Wigner analysis of the previous equations, as started in Part I, cf. [14]. Namely, the classical Wigner distribution is extended by considering a class of time-frequency representations constructed as images of metaplectic operators acting on symplectic matrices $\mathcal{A}\in Sp(2d,\mathbb{R})$. Sub-classes of these representations, related to covariant symplectic matrices, reveal to be particularly suited for the time-frequency study of the Schrödinger evolution. This testifies the effectiveness of this approach for such equations, highlighted by the development of a related wave front set. We first study the properties of $\mathcal{A}$-Wigner representations and related pseudodifferential operators needed for our goal. This approach paves the way to new quantization procedures. As a byproduct, we introduce new quasi-algebras of generalized metaplectic operators containing Schrödinger equations with more general potentials, extending the results contained in the previous works [8,9].
