... the principal coefficients apqare continuous in x ∈ Ω uniformly with respect to t ∈ [0, ∞) and the constant a0 in (1.1) is independent of t,byrepeating the proof of Garding’s inequality [2, p. 44], ... s-matrices of measurable, bounded in Ω∞, complex functions,apq=(−1) |p| + |q| a∗qp. Suppose that apqare continuous in x ∈ Ω uniformly with On the Smoothness of Solutions 139(−1)mm |p| , |q| =0D p apq(x, ... coordinate system on Sn−1. The principal part of theoperator L(x, t, D) at origin 0 can be written in the formL0(0,t,D)=r−2m Q( ω, t, rDr,Dω),Dr=i∂∂r,where Q is a linear operator with...