Geometry of Spectral Problems
by
Hongyou Wu
Department of Mathematics, NorthIllinois University, Delkalb, IL 60115

We are concerned with spectral problems for linear differential operators. Geometric structures are introduced on various spaces of boundary conditions used in these problems, especially the space of self-adjoint boundary conditions. These structures form the base for studying the dependence of the spectrum of a general spectral problem on the boundary condition in the problem, and reveal many new properties of the spectrum. In this talk, we will explain these structures and demonstrate their applications, such as a normal form of self-adjoint boundary conditions for orders greater than or equal to 3, the space of left-definite boundary conditions, level surface of the n th eigenvalue, infinite band for non-real eigenvalues, etc.

Date received: March 21, 2003