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.

From the reviews: It consists of five chapters, and all chapters close with a great number of additional explanatory notes connecting the results with a thorough bibliography. It contains a rich list of 210 references of carefully selected old and new works, which, also, might be a good source to graduates for further study of the theory of periodic differential operators. (George Karakostas, zbMATH, Vol. 1267, 2013)

Inhalt

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