21 research outputs found

    Two classes of generalized functions used in nonlocal field theory

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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 S0S^0 (which is the Fourier transform of the Schwartz space D\mathcal D) and using test functions in the Gelfand-Shilov spaces Sα0S^0_\alpha. We prove that every functional defined on S0S^0 has the same carrier cones as its restrictions to the smaller spaces Sα0S^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.Comment: AMS-LaTeX, 12 pages, no figure
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