Mixed boundary value problems for concentric cylinders—an algebraic operator formulation

Abstract

Unitary operators are introduced which act on the Fourier transforms of the boundary values on concentric cylinders of a harmonic function in E ₃. The boundary values on the concentric cylinders are determined from given mixed boundary conditions on the same cylinders, and the solution for them is expressed explicitly and simply through the use of these unitary operators plus certain other self adjoint positive operators. The boundary values on the cylinders then determine the harmonic function everywhere in E ₃.