“…The main problem of studies in [4,15] is the Cauchy problem for a system of evolution equations with partial derivatives u t = K(t, x, ∂)u + f (t, x), x ∈ Ω ⊂ R q , t > 0, u| t=0 = ϕ ∈ B, (1.1) where B is some Banach space. Let us consider the Heisenberg-Weyl algebra…”