Spectral Structure of Periodic Elliptic Operators

This chapter constitutes a significant part (both in terms of its importance and size) of the book. Here, problems of spectral theory are addressed. The basic fact about the essential self-adjointness of elliptic periodic operators is established first. Then, the reader finds the results on the structure of the spectrum (absolute continuous, pure point, and singular continuous spectra), the presence and number of spectral gaps, spectral asymptotics, Shnol’-type theorem, Floquet–Bloch eigenfunctions, inverse problems, and more.