On Some Classes of Differential Operators Generating Analytic Semigroups *

Inspired by the fundamental papers by Feller [10], Clément and Timmermans [3] and Timmermans [17], we began a systematic study of the analyticity (in different function spaces) of the C_o -semigroups generated by second order differential operators of the type A u : = α u ″ + β u ′ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187810/28005645-324c-4d25-a9e4-00a49a74dffd/content/equ_chapter8_105_1.tif"/> where α and β are real-valued continuous functions in an interval I of R, α(x) > 0 in the interior of I and α is allowed to vanish at the endpoints (see e.g. [5], [6], [7], [8]). Valuable contributions to this study were also given by Campiti, Metafune and Pallara [2] and Metafune [14].