Existence and uniqueness theorems of equivalent differential operators of thin wire integral equations

It is shown that for each integral equation of the thin wire type, there exists a unique differential equation, the solution of which is identical to the integral equation, if the same boundary conditions of the integral equation are applied to the differential equation. The existence and uniqueness theorems are proved. Those theorems are normally applied to the solutions of operators. The novelty of the present theorems is that they are applied to the operators themselves. The application of those theorems to the circuit component extraction from the dynamic solution is presented.