Caltech/UCLA Joint Analysis Seminar

UCLA MS 6627

Let $X$ be a compact manifold with the boundary $Y$ and $R(k)$ be a Dirichlet-to-Neumann operator: $R (k):f to partial_n u |_Y$ where u solves $$ (Delta+k^2) u=0, u|_Y=f. $$ We establish asymptotics as $kto infty$ of the number of eigenvalues of $k^{-1}R (k)$ between $a$ and $b$.

We will discuss tools, used to solve this problem: sharp semiclassical spectral asymptotics and Birman-Schwinger principle.

This is a joint work with Andrew Hassell, Australian National University.