On quasi-periodic lattice Schrödinger operators.
The aim of the paper is to review a number of developments over the recent years on the following topics: (1) spectrum and eigenfunctions of Schrödinger operators on \(\mathbb{Z}\) and \(\mathbb{Z}^D\) with a quasi-periodic potential, (2) linear Schrödinger equations with time periodic potential, (3) KAM theory for nonlinear PDE. The paper mainly surveys the works of the author and his collaborators. Compared with earlier research in the areas listed above, there are two new methods extensively used in the contributions considered: (1) subharmonic function techniques, (2) the theory of semi-algebraic sets.
scientific article; zbMATH DE number 2077708