Carrier cones of analytic functionals

Abstract

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 $S_{\alpha }^0$, but their derivation is more sophisticated because $S^0(K)$ are not DFS spaces and have more complicated topological structure.

10 pages, LaTeX2e, no figures; minor typos corrected

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• General Properties of Noncommutative Field Theories
• PCT, spin and statistics, and analytic wave front set
• Non-Localizability and Asymptotic Commutativity
• Towards a Generalized Distribution Formalism for Gauge Quantum Fields
• A New Derivation of the CPT and Spin-Statistics Theorems in Non-Commutative Field Theories

Cited by in corpus (3)

• Axiomatic formulations of nonlocal and noncommutative field theories
• Decomposition theorems and kernel theorems for a class of functional spaces
• On kernel theorems for (LF)-spaces