Abstract. A new proof of a representation result of weakly continuous local semigroups of symmetric operators obtained by A. Klein and L. J. Landau is given. As an application, a representation result as Laplace transform of operator valued functions of positive type, which generalizes a result given by D. V. Widder, is obtained.
AMS Subject Classification
(1991): 47D03, 47B25, 44A10
local semigroup of operators,
Received June 12, 2017, and in revised form September 3, 2017. (Registered under 40/2017.)