Eigenvalues of Non-selfadjoint Operators: A Comparison of Two Approaches
By Michaela Demuth, Marcel Hansmann, Guy Katriel. 2012
70 citations recorded by the source corpus.
The central problem we consider is the distribution of eigenvalues of closed linear operators which are not selfadjoint, with a focus on those operators which are obtained as perturbations of selfadjoint linear operators. Two methods are explained and elaborated. One approach uses complex analysis to study a holomorphic function whose zeros can be identified with the eigenvalues of the linear operator. The second method is an operator theoretic approach involvingthe numerical range. General results obtained by the two methods are derived and compared. Applications to non-selfadjoint Jacobi and Schrodinger operators are considered. Some possible directions for future research are discussed.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0aab1182cb0518711bd1b05d3932258be8cb73fe
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In Applied Mathematics
- Barry Simon
- Rupert L. Frank
- David Damanik
- Doron S. Lubinsky
- N. H. Bingham
- Alexander Pushnitski
- David Damanik
- Bartłomiej Dyda
In Mathematical Physics
- Barry Simon
- Rupert L. Frank
- Doron S. Lubinsky
- David Damanik
- David Damanik
- Alexander Pushnitski
- Vilmos Totik
Citations in the corpus
- Eigenvalue bounds for Schrödinger operators with complex potentials. II (2015, background): “The situation for sums of eigenvalues is less understood and we refer to [9, 18, 3, 6, 11] and references therein for results and open questions in this direction.”