Nuclear spaces, which arise naturally in the study of differential and convolution equations, were introduced and extensively studied by A. Grothendiek. Many of the more important of these spaces, e.g the fully nuclear spaces, have additional structure such as an absolute basis and easily characterised Gaussian measures, but like all infinite dimensional topological vertor spaces they do not admit a translational invariant measure. We show, using the above two properties, that holomorphic functions of exponential growth on fully nuclear spaces admit integal representations with respect to a suitably chosen Gaussian measure.
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Last updated 1 May 2008. This page was created and is maintained by Stephen Wills (s.wills@ucc.ie).