Carrier cones of analytic functionals

Details Carrier cones of analytic functionals Carrier cones of analytic functionals

2005-07-06

arxiv.org/abs/math-ph/0507011v2

Physics

Mathematical Physics

10 pages, LaTeX2e, no figures; minor typos corrected

Scientific paper

We prove that every continuous linear functional on the space $S^0(R^d)$ consisting of the entire analytic functions whose Fourier transforms belong to the Schwartz space $\mathcal D$ has a unique minimal carrier cone in $R^d$, which substitutes for the support. The proof is based on a relevant decomposition theorem for elements of the spaces $S^0(K)$ associated naturally with closed cones $K\subset R^d$. These results, essential for applications to nonlocal quantum field theory, are similar to those obtained previously for functionals on the Gelfand-Shilov spaces $S^0_\alpha$, but their derivation is more sophisticated because $S^0(K)$ are not DFS spaces and have more complicated topological structure.

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