The Weyl Criterion for the Spectrum


Zhiqin Lu

10:30:00 - 12:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk I prove a generalization of Weyl's criterion for the spectrum of a self-adjoint nonnegative operator on a Hilbert space. We will use the new criterion to study the variation in the spectrum under continuous perturbations of the operator.  In the particular case of the Laplacian on differential k-forms over an open manifold we will use these analytic tools to find significantly stronger results for its spectrum  including its behavior under a continuous deformation of the metric of the manifold. This is joint with N. Charalambous.