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Two classes of generalized functions used in nonlocal field theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 2, pp. 195-210
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We elucidate the relation between the two ways of formulating causality in nonlocal quantum field theory: using analytic test functions belonging to the space $S^0$ (which is the Fourier transform of the Schwartz space $\mathcal D$) and using test functions in the Gelfand–Shilov spaces $S^0_\alpha$. We prove that every functional defined on $S^0$ has the same carrier cones as its restrictions to the smaller spaces $S^0_\alpha$. As an application of this result, we derive a Paley–Wiener–Schwartz-type theorem for arbitrarily singular generalized functions of tempered growth and obtain the corresponding extension of Vladimirovs algebra of functions holomorphic in a tubular domain.
Keywords: nonlocal quantum fields, causality, Wightman functions, analytic functionals, Paley–Wiener–Schwartz-type theorems.
Mots-clés : Hörmanders estimates 
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     title = {Two classes of generalized functions used in nonlocal field theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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M. A. Soloviev. Two classes of generalized functions used in nonlocal field theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 2, pp. 195-210. http://geodesic.mathdoc.fr/item/TMF_2005_143_2_a1/

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