Abstract:
We consider the Cauchy problem for harmonic functions outside some disc
in the plane with the Cauchy data on an interval. We obtain simple formulae
for singular values of the operator solving this Cauchy problem and explicit
bounds on the difference between the exact and truncated operators. For a
typical particular geometry we compute numerically these singular values and
analyse their dependence on the size of the interval, on its distance to the
disc, etc. As a consequence, we can tell how many parameters of the harmonic
function (or of a source producing this function) can be found from the Cauchy
data.