The sector of analyticity of nonsymmetric submarkovian semigroups generated by elliptic operators

Abstract

We prove that a lower bound for the angle θ p of the sector of analyticity of not necessarily symmetric submarkovian semigroups generated by second order elliptic operators in divergence form or by Ornstein–Uhlenbeck in L μ p is given by cot θ p = ( p − 2 ) 2 + p 2 ( cot θ 2 ) 2 / ( 2 p − 1 ) . If the semigroup is symmetric then we recover known results. In general, this lower bound is optimal. To cite this article: R. Chill et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).