论文标题
用于操作员值和等效的操作员值符号的磁性分量分化符号
A Magnetic Pseudodifferential Calculus for Operator-Valued and Equivariant Operator-Valued Symbols
论文作者
论文摘要
在这本专着中，我们为运营商价值和等效的运算符值的功能和分布开发了磁性差异理论。这些发现在数学物理学中发现了很多应用，包括用于慢速系统和扰动周期性操作员的严格扰动理论。然而，迄今为止缺少一本系统的论文。尽管可以在附录中零散地找到许多结果，并且作为其他文章中的草图，但本文确实包含了新的结果。例如，我们已经针对这两种情况建立了比尔斯型换向器标准，这意味着（e earivariant）selfadjoint-operator-parewarew arewareed，Elliptichörmander符号存在Moyal分解，并允许一个人构建功能性计算。此外，我们给出了磁性假数算子（本地）跟踪类的功能的标准。我们对本文的目的是三个方面：（1）创建同事可以提到的单一扎实的作品。 （2）是教学和精确的。 （3）给出了一种直接的策略，以将其估算到模棱两可的案件中扩展结果，并指出一些需要牢记的警告和陷阱。
In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics, including in rigorous perturbation theory for slow-fast systems and perturbed periodic operators. Yet, a systematic treatise was hitherto missing. While many of the results can be found piecemeal in appendices and as sketches in other articles, this article does contain new results. For instance, we have established Beals-type commutator criteria for both cases, which then imply the existence of Moyal resolvents for (equivariant) selfadjoint-operator-valued, elliptic Hörmander symbols and allows one to construct functional calculi. What is more, we give criteria on the function under which a magnetic pseudodifferential operator is (locally) trace class. Our aims for this article are three-fold: (1) Create a single, solid work that colleagues can refer to. (2) Be pedagogical and precise. And (3) give a straightforward strategy for extending results from the operator-valued to the equivariant case, pointing out some caveats and pitfalls that need to be kept in mind.
