Analytic Feller semigroups via hypergeometric series (Q2516272)

\textit{W. Feller} [Ann. Math. (2) 55, 468--519 (1952; Zbl 0047.09303)] showed that the operator \(A\) defined by \(Au(x) = x(1-x)u''(x)\) with Wentzell boundary condition (\(Au(x)=0\) for \(x = 0, 1\)) generates a strongly continuous contraction semigroup generally called the Feller semigroup. \textit{G. Metafune} [Stud. Math. 127, No. 3, 251--276 (1998; Zbl 0901.35048)] proved that this semigroup is actually analytic. In the present paper, the authors use a different but simpler method, making use of the properties of hypergeometric functions to establish the same result. They show that this simple method can be used to prove that a semigroup generated by a more general degenerate second order differential operator with Wentzell boundary conditions is analytic.