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Two classes of generalized functions used in nonlocal field theory

Michael A. Soloviev
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Abstract

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 Vladimirov's algebra of functions holomorphic on a tubular domain.

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Michael A. Soloviev. 2006-05-24. Two classes of generalized functions used in nonlocal field theory. https://doi.org/10.1007/s11232-005-0096-8

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