Two Classes of Generalized Functions Used in Nonlocal Field Theory
نویسنده
چکیده
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 (which is the Fourier transform of the Schwartz space D) and using test functions in the Gelfand-Shilov spaces S α. We prove that every functional defined on S 0 has the same carrier cones as its restrictions to the smaller spaces S α. 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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