A Dirichlet-to-Robin Transform for Semiclassical Spectral Theory 


    A simple transformation converts a solution of a PDE with a 
Dirichlet boundary condition to a function satisfying a Robin 
(generalized Neumann) condition.  In the simplest cases this 
observation enables the exact construction of the Green functions 
for the wave, heat, and Schrodinger problems with a Robin 
boundary condition.  The resulting physical picture is that the 
field can exchange energy with the boundary, and a delayed 
reflection from the boundary results.  In more general situations
the method allows at least approximate and local construction of 
the appropriate reflected solutions, and hence a "classical path" 
analysis of the Green functions that carries spectral 
information.  Some of this work was done in collaboration with 
Joel Bondurant, a recent M.S. graduate.