Research Group on Spectral Theory of Differential Operators

Participants

At LSU

Stephen Shipman

Rui Han

Lee Fisher

Jorge Villalobos

Elsewhere

Wei Li, DePaul University

Wencai Liu, TX A&M

Gregory Berkolaiko, TX A&M

Etc.

Some Literature

1. N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, Dover, 1993, replication of the edition of F. Ungar Publishing, NY, 1961, 1963.
2. B. Malcolm Brown, Michael S. P. Eastham, and Karl Michael Schmidt, Periodic Differential Operators, Birkhäuser 2013.
3. David Cox, John Little, and Donal O'Shea, Ideals, Varieties, and Algorithms, Springer, 2007.
4. P. Deift and E. Trubowitz, Inverse Scattering on the Line, Communications on Pure and Applied Mathematics XXXII (1979) 121-251.
5. G. Freiling and V. Yurko, Inverse Sturm-Liouville Problems and Their Applications, Nova Science Publishers, 2001.
6. Peter Kuchment, An overview of periodic elliptic operators, Bull. Am. Math. Soc. Vol. 53, No. 3 (2016) 343-414.
7. Erich Müller-Pfeiffer, Spectral Theory of Ordinary Differential Operators, Ellis Horwood Ltd., 1981.
8. Jürgen Pöschel and Eugene Trubowitz, Inverse Spectral Theory, Pure and Applied Mathematics, Vol. 130, Academic Press, 1987.
9. Michael Reed and Barry Simon, Methods of Modern Mathematics: Vol. I Functional Analysis, Vol. II Fourier Analysis and Self-Adjointness, Vol. III Scattering Theory, Vol. IV Analysis of Operators, excerpts from Vol. I (spectral theorem), Vol. II (self-adjoint extensions), Academic Press, 1980.
10. Stephen P. Shipman, Reducible Fermi Surfaces for Non-symmetric Bilayer Quantum-Graph Operators arXiv:1712.03315 (2017).