Remarks on Generators of Analytic Semigroups.

This paper contains two new characterizations of generators of analytic semigroups of linear operators in a Banach space. These characterizations do not require use of complex numbers. One is used to give a new proof that strongly elliptic second order partial differential operators generate analytic semigroups in L superscript p, 1 p infinity, while the sufficient condition in the other characterization is meaningful in the case of nonlinear operators. (Author)