Geodesic
Nuclear Spaces of Generalized Test Functions
Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 269-273

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It is well known that a large proportion of the locally convex spaces encountered in distribution theory are nuclear (Grothendieck [4], Treves [10], Schaeffer [8].) In [1] Beurling introduced spaces of test functions more general than those previously used. In this paper we shall show that many of these spaces, and resulting spaces of distributions, are also nuclear spaces. 
Millington, H. Nuclear Spaces of Generalized Test Functions. Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 269-273. doi: 10.4153/CMB-1973-045-x
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     author = {Millington, H.},
     title = {Nuclear {Spaces} of {Generalized} {Test} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {269--273},
     year = {1973},
     volume = {16},
     number = {2},
     doi = {10.4153/CMB-1973-045-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-045-x/}
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