Massimo Bertini, Diego Noja, Andrea Posilicano
WAVE EQUATIONS WITH POINT INTERACTIONS IN FINITE ENERGY SPACES 
(54K, AMSTEX)

ABSTRACT.  Given the abstract wave equation $\ddot\phi-\Delta_\alpha\phi=0$, 
where $\Delta_\alpha$ is the Laplace operator with a point interaction 
of strength $\alpha$, we define and study $\bar W_\alpha$, the 
associated wave generator in the phase space 
of finite energy states. We prove the existence of the phase flow 
generated by $\bar W_\alpha$, and describe its most relevant properties 
with particular emphasis on the associated symplectic 
structure and scattering theory.