On the discrete spectrum of non-selfadjoint operators

By Michaela Demuth, Marcel Hansmann, Guy Katriel. 2009

98 citations recorded by the source corpus.

We prove quantitative bounds on the eigenvalues of non-selfadjoint unbounded operators obtained from selfadjoint operators by a perturbation that is relatively-Schatten. These bounds are applied to obtain new results on the distribution of eigenvalues of Schroedinger operators with complex potentials.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/49abfcf8ffa9cfd4e684ba5e2b2b8398cf3db75f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Rupert L. Frank
2. Julien Sabin
3. Bartłomiej Dyda

In Atomic and Molecular Physics, and Optics

1. Julien Sabin
2. Rupert L. Frank

In Mathematical Physics

1. Rupert L. Frank
2. Julien Sabin
3. Marcel Hansmann
4. Guy Katriel
5. Michaela Demuth

Citations in the corpus

• Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates (2014, methodology): “Eigenvalues bounds for Schr¨odinger operators with complex-valued potentials have been the topic of many works, see for instance [1, 11, 23, 5, 10] and references therein.”
• Eigenvalues of Non-selfadjoint Operators: A Comparison of Two Approaches (2012, background): “We note that the results to follow can be regarded as refinements of our earlier work [9] (see also [24]).”