Option A inverse and its constraints

The classical composition and its polarization are

Here $f\in {C_c}^{\infty }((t_0,T)\times {\mathbb{R}}^3)$. Newton potentials of Schwartz sources are smooth with polynomially bounded derivatives. Finite-time wave propagation preserves such bounds. Multiplication by derivatives of a Schwartz scalar solution gives Schwartz response sources. The finite Duhamel integrals therefore define (eq:cubicclassical).

Figure fig:Option-A-composition displays the inverse used in the cubic composition and the distinct comparison prescription.