Polyharmonicity: Robin functions

For a planar domain of the complex plane, the area integral operator with harmonic Green function as kernel provides a particular solution to the Poisson equation. This operator serves to convoluting harmonic Green functions with itself resulting in a variety of hybrid polyharmonic Green functions. Besides Green also Neumann and Robin functions are involved as other polyharmonic Green functions of lower order, e.g. the polaharmonic Green-Almansi function, could be incorporated.A broad class of polyharmonic Green functions of different kinds is attained by convoluting harmonic Robin functions, because Robin functions depend on two real parameters. As they are themselves interpolations between Green and Neumann functions, many particular cases are covered. They are useful to solve polyharmoic Robin boundary value problems for higher order Poisson equations under proper solvability conditions, Dirichlet, Requier, and Neumann problems included.