Singularities and the Rayleigh Hypothesis for Solutions to the Helmholtz Equation

Possible and actual singularities in the analytic continuationof the solution to the Dirichlet problem for the two-dimensionalHelmholtz equation are studied in order to investigate the Rayleighhypothesis of scattering theory. The procedure uses a representationfor the solution to the analytic Cauchy problem and relatesone type of singularity in the Schwarz function associated withthe boundary curve to singularities in the solution. The resultsprovide confiration of criteria for the validity of the Rayleighhypothesis that have been given by van den Berg and Fokkema.