论文标题
正式的振荡分布
Formal oscillatory distributions
论文作者
论文摘要
我们介绍了一点点支持的振荡正式分布的概念。我们证明，当它是具有一定非平稳属性的振荡分布时，正式的振荡积分是正式的分布。我们给出了一种算法，该算法从相应的正式分布中恢复了在临界点处正式振荡积分不可或缺的内核的无限顺序。 We also prove that a star product $\star$ on a Poisson manifold $M$ is natural in the sense of Gutt and Rawnsley if and only if the formal distribution $f \otimes g \mapsto (f \star g)(x)$ is oscillatory for every $x \in M$.
We introduce the notion of an oscillatory formal distribution supported at a point. We prove that a formal distribution is given by a formal oscillatory integral if and only if it is an oscillatory distribution that has a certain nondegeneracy property. We give an algorithm that recovers the jet of infinite order of the integral kernel of a formal oscillatory integral at the critical point from the corresponding formal distribution. We also prove that a star product $\star$ on a Poisson manifold $M$ is natural in the sense of Gutt and Rawnsley if and only if the formal distribution $f \otimes g \mapsto (f \star g)(x)$ is oscillatory for every $x \in M$.
