The theory of semigroups with weak singularity and its applications to partial differential equations (Q909967)

The paper contains an exposition of the theory of semigroups of linear operators U(z) which are analytic in the sector \(\{z=t+is\), \(z\neq 0\), \(| \arg z| <\pi /2-\epsilon \}\), \(0<\epsilon <\pi /2\) and may have singularity at the origin such that \(\| U(z)\| \leq M/| z|^{\theta}\). The application to the theory of subelliptic initial- boundary value problems for linear parabolic differential equations of second order are given.