A Schauder and Riesz Basis Criterion for Non-Self-Adjoint Schr\

By Fritz Gesztesy, V. Tkachenko. 2011

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Under the assumption that V∈L2([0,π];dx), we derive necessary and sufficient conditions in terms of spectral data for (non-self-adjoint) Schrodinger operators −d2/dx2+V in L2([0,π];dx) with periodic and antiperiodic boundary conditions to possess a Riesz basis of root vectors (i.e., eigenvectors and generalized eigenvectors spanning the range of the Riesz projection associated with the corresponding periodic and antiperiodic eigenvalues). We also discuss the case of a Schauder basis for periodic and antiperiodic Schrodinger operators −d2/dx2+V in Lp([0,π];dx), p∈(1,∞).

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7226ee820d5712b821e5af513eab4b4db94ce5a5

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In Computational Theory and Mathematics

1. M. Malamud
2. L. Oridoroga
3. Dmitry Yakubovich
4. A. Baranov

In Mathematical Physics

1. M. Malamud
2. L. Oridoroga
3. Jussi Behrndt
4. Dmitry Yakubovich
5. A. Baranov
6. Olaf Post

Citations in the corpus

• On the completeness of root subspaces of boundary value problems for first order systems of ordinary differential equations (2012, background): “In particular, in [17], as well as in the recent preprint by P.”