Holomorphic one-parameter semigroups of bounded linear operators on Lp(Rn), 1 < p < ∞, generated by strongly M-elliptic pseudo-differential operators

Abstract

For a M-elliptic pseudo-differential operator on $R^n$, we give a sufficient condition on its symbol to ensure that it is the infinitesimal generator of a holomorphic one-parameter semigroup of bounded linear operators on $L^p\left(R^n\right)$, $1<p<\infty$.