Carrier cones of analytic functionals

2005/07/06 by M. A. Soloviev, Soloviev, M. A.
Mathematics · Physics and Astronomy · #32C81 (Primary) #46E10 #46F05 (Secondary) #46F15 #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #math-ph #math.FA #math.MP #msc:32C81 #msc:46E10 #msc:46F05 #msc:46F15

paper · pdf · doi:10.48550/arxiv.math-ph/0507011

10 pages, LaTeX2e, no figures; minor typos corrected

openalex publication_date 2005/07/06 · arxiv created 2005/07/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every continuous linear functional on the space S⁰(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 S⁰(K) associated naturally with closed cones K⊂ 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 S⁰_α, but their derivation is more sophisticated because S⁰(K) are not DFS spaces and have more complicated topological structure.

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