Mathematical Physics Seminar

The talk is about asymptotics of the counting function N(t) for the
Laplace operator on an open set in 3 dimensions. We prove that N(t) = C
t^3/2 + O(t) as t tends to infinity, which is known to be sharp. The proof
is based on the observation that the cosine transform of the spectral
function satisfies a wave equation. The solution operator of this wave
equation is then approximated by a method due to Hadamard. Finally we
employ a Tauberian theorem to translate the results back to information
about the counting function.
The talk is based on work by Robert Seeley.