Event

Talk
Compact group actions and spectral asymptotics for pseudodifferential operators on bounded domains in R^n
25 Jun 2007, 16:30 – 17:30

Let G be a compact group of isometries acting on n-dimensional Euclidean space, and X a bounded domain which is transformed into itself under the action of G. Consider a symmetric, classical pseudodifferential operator A with G-invariant symbol, and assume that it is semi-bounded from below. The spectrum of the Friedrichs extension of the restriction of A to X is discrete, and employing the method of the stationary phase, we derive asymptotics for the number of eigenvalues for each isotypic component, giving also an estimate for the remainder term. Since the considered critical set is a singular variety, we use resolution of singularities in order to apply the stationary phase theorem.

Related to:

• Pablo Ramacher