INTEGRAL REPRESENTATION OF POSITIVE OPERATOR ON INFINITE DIMENSIONAL SPACE OF ENTIRE FUNCTIONS

In this paper, we give a new criterion for positivity of generalized functions and positive operators on test functions space of entire function on the dual of a nuclear space N' and with theta order growth condition, denoted by F-theta(N'). This definitions are used to prove that every positive operator has integral representation given by positive Radon measure and these measures are characterized by integrability conditions. This new criterion of positivity can be easily applied to several examples.