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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.
DOI: 10.14232/actasm-017-040-x
AMS Subject Classification
(1991): 47D03, 47B25, 44A10
Keyword(s):
local semigroup of operators,
symmetric,
self-adjoint,
infinitesimal generator
Received June 12, 2017, and in revised form September 3, 2017. (Registered under 40/2017.)
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