Commutators, spectral trace identities, and universal estimates for eigenvalues
Commutators, spectral trace identities, and universal estimates for eigenvalues
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DOI：
10.1006/jfan.2001.3913
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发表时间：
2001-02
影响因子：
1.7
通讯作者：
M. Levitin;L. Parnovski
中科院分区：
文献类型：
--
作者：
M. Levitin;L. Parnovski
Using simple commutator relations, we obtain several trace identities involving eigenvalues and eigenfunctions of an abstract self-adjoint operator acting in a Hilbert space. Applications involve abstract universal estimates for the eigenvalue gaps. As particular examples, we present simple proofs of the classical universal estimates for eigenvalues of the Dirichlet Laplacian, as well as of some known and new results for other differential operators and systems. We also suggest an extension of the methods to the case of non-self-adjoint operators.
