SOLUTIONS OF BOUNDARY-VALUE PROBLEMS FOR THE HELMHOLTZ EQUATION IN SIMPLY CONNECTED DOMAINS OF THE COMPLEX PLANE

摘要

The bases in the spaces of functions analytic in simply connected domains are constructed with the help of conformal mappings of these domains onto a circle. The obtained basis functions are biorthogonal to the Faber polynomials. By using the expansions of analytic functions in series in systems of basis functions, we determine the solutions of boundary-value problems for the Helmholtz equation whose boundary values coincide with the boundary values of these functions.