Abstract
Let S′ be the space of tempered distributions on . In this paper we introduce a test functional space E∞ consisting of real analytic functions on S′ of exponential type of order one which is shown to be equivalent to the Kondratiev space. Then, using a probabilistic approach, we give an elementary proof for the Kondratiev–Streit–Weaterkamp theorem, that is, every positive generalized white noise functional on E∞ can be represented by a Borel measure on S′ satisfying exponential integrability.
†Results presented here have partially been presented in the Ph.D dissertation of the second author.
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ACKNOWLEDGMENT
First author supported by the National Science Council of R.O.C. (Taiwan).
Notes
†Results presented here have partially been presented in the Ph.D dissertation of the second author.