Degenerate differential equations and modified Szász-Mirakjan operators (Q708764)

This paper deals with operators \(L\) defined by \[ (Lu)(x) = xu'' (x) + \beta(x)u' (x) + \tau(x)u(x),\quad x \in [0, \infty]. \] Conditions are sought under which this operator generates a \(C_0\)-semigroup. Various weighted spaces of continuous functions for the domain of \(L\) are considered, as are Wentzell-type boundary conditions. The authors prove several semigroup generation theorems under a variety of assumptions. The paper is particularly useful for the reader who is interested in semigroup generation by singular differential operators.