Invariant subspaces of elliptic systems I: pseudodifferential projections
Invariant subspaces of elliptic systems I: pseudodifferential projections
复制标题
椭圆系统的不变子空间 I：伪微分投影
DOI：
10.1016/j.jfa.2022.109402
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发表时间：
2021
影响因子：
1.7
通讯作者：
D. Vassiliev
中科院分区：
文献类型：
--
作者：
Matteo Capoferri;D. Vassiliev
考虑椭圆型自伴伪微分算子A作用在闭流形M上的m列半密度上，其主符号具有单特征值。我们证明了与算子A交换的m正交伪微分投影的存在性和唯一性，并提供了计算其全符号的算法，以及其子主符号的显式封闭公式。在A模C∞（M）的作用下，伪微分投影将L2（M）分解为不变子空间.此外，他们允许我们分解成m个不同的符号确定的伪微分算子。最后，我们代表的模和Heaviside函数的运营商A的伪微分投影和讨论物理上有意义的例子。
Consider an elliptic self-adjoint pseudodifferential operator A acting on m-columns of half-densities on a closed manifold M, whose principal symbol is assumed to have simple eigenvalues. We show existence and uniqueness of m orthonormal pseudodifferential projections commuting with the operator A and provide an algorithm for the computation of their full symbols, as well as explicit closed formulae for their subprincipal symbols. Pseudodifferential projections yield a decomposition of L 2 (M) into invariant subspaces under the action of A modulo C∞(M). Furthermore, they allow us to decompose A into m distinct sign definite pseudodifferential operators. Finally, we represent the modulus and the Heaviside function of the operator A in terms of pseudodifferential projections and discuss physically meaningful examples.
黎曼流形上的几何波传播器
影响因子：
0.7
作者：
Capoferri Matteo
通讯作者：
Capoferri Matteo
作为物质场的时空微分同胚
影响因子：
1.3
作者：
Capoferri M
通讯作者：
Capoferri M