Abstract :
In this article, we extend the study of generalized point interactions to the
periodic case, and we investigate analogues of the Kronig]Penney model for the
class of point interactions introduced in joint work with P. Chernoff. In addition to
periodic d- and d X-potentials, which follow as special cases, several examples are
studied in detail. In general, the models under consideration are shown to have
purely absolutely continuous spectrum, and in some cases all gaps in the spectrum
close.
