DISCRETE OBSERVABILITY OF A GENERALIZED WAVE-EQUATION ON A COMPACT HOMOGENEOUS SPACE

The problem of discrete observation of the wave equation on compact ho mogeneous spaces is considered. In contrast to previous work on the he at equation, an additional initial condition requires the use of an ex tended sampling scheme and changes the structure of the problem. The c onditions under which approximate discrete observability holds are pro ven, as is the existence of samples which satisfy those conditions. Ac uity of observation is established, providing general analytic bounds on the error in using only finitely many samples. Also, under certain strict conditions which depend on the sample points, the error is show n to go to zero through a set of Sobolev conditions. The results are s omewhat similar in statement to those obtained for bounded domains in Euclidean space in an earlier paper, but the methods used to obtain th em are different and rely heavily on the representation theory of the underlying space.