$C_0$-semigroups generated by second order differential operators
Volume 116 / 2016
Annales Polonici Mathematici 116 (2016), 57-66
MSC: Primary 47D06; Secondary 47D07, 47F05, 47B65.
DOI: 10.4064/ap3737-12-2015
Published online: 3 December 2015
Abstract
Let $W(u)(x)=\frac {1}{2}x^a(1-x)^bu''(x)$ with $a,b\geq 2$. We consider the $C_0$-semigroups generated by this operator on the spaces of continuous functions, respectively square integrable functions. The connection between these semigroups together with suitable approximation processes is studied. Also, some qualitative and quantitative properties are derived.
