Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-01-03
Commun.Math.Phys. 184 (1997) 579-596
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, LaTeX, submitted to Commun.Math.Phys
Scientific paper
10.1007/s002200050074
We show that a considerable part of the theory of (ultra)distributions and hyperfunctions can be extended to more singular generalized functions, starting from an angular localizability notion introduced previously. Such an extension is needed to treat gauge quantum field theories with indefinite metric in a generic covariant gauge. Prime attention is paid to the generalized functions defined on the Gelfand-Shilov spaces $S_\alpha^0$ which gives the widest framework for construction of gauge-like models. We associate a similar test function space with every open and every closed cone, show that these spaces are nuclear and obtain the required formulas for their tensor products. The main results include the generalization of the Paley--Wiener--Schwartz theorem to the case of arbitrary singularity and the derivation of the relevant theorem on holomorphic approximation.
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