Two classes of generalized functions used in nonlocal field theory

Details Two classes of generalized functions used in nonlocal field theory Two classes of generalized functions used in nonlocal field theory

2006-05-24

arxiv.org/abs/math-ph/0605065v1

Theor.Math.Phys. 143 (2005) 651-663; Teor.Mat.Fiz. 143 (2005) 195-210

Physics

Mathematical Physics

AMS-LaTeX, 12 pages, no figures

Scientific paper

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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