Periodic Elliptic Partial Differential Operators

Peter Kuchment is the Arthur George and Mary Emolene Owen Chair and Distinguished Professor at Texas A & M University. His research interests include partial differential equations, mathematical physics, geometric analysis, inverse problems, tomography and medical imaging, material science, and math education. He is the author of the books `Floquet Theory for Partial Differential Operators' (1993), `Introduction to Quantum Graphs' (2013), 'The Radon Transform and Medical Imaging' (2014) and 'Liouville-Riemann-Roch Theorems on Abelian Coverings' (2021).

• Preface; Introduction; Tentative contents of the planned sequel; 1. Periodic ordinary differential operators; 2. Multidimensional periodicity: lattices, fundamental domains, Fourier series; 3. Floquet transform and direct integral decomposition; 4. Dispersion relations, Bloch, Fermi and Floquet varieties; 5. Spectral structure of periodic elliptic operators; 6. Localized perturbations of periodic operators; 7. Wannier functions; 8. Operators on Abelian coverings of compact manifolds; Appendix A. Some information from complex analysis; Appendix B. Some information from functional analysis and operator theory; Appendix C. Operator-functions; Appendix D. Banach (locally trivial) vector bundles; Appendix E. The Landis conjecture; Appendix F. Proofs of some technical statements; References; Index.