Periodic Differential Operators

This book surveys the theoretical foundations of periodic differential operators, and proceeds to offer a coherent review of recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations.

Periodic differential operators have a rich mathematical theory as well as important physical applications. They have been the subject of intensive development for over a century and remain a fertile research area. This book lays out the theoretical foundations and then moves on to give a coherent account of more recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations. The book will be valuable to advanced students and academics both for general reference and as an introduction to active research topics.

Comprehensive treatment of one-dimensional periodic systems from the differential equation, boundary-value problem and operator-theoretic points of view Unified analysis of periodic Sturm-Liouville- and Dirac-type operators by the use of oscillation methods Study of perturbed periodic problems Includes supplementary material: sn.pub/extras

Inhalt

Preface.- 1 Floquet Theory.- 2 Oscillations.- 3 Asymptotics.- 4 Spectra.- 5 Perturbations.