2006/12/25 by A. G. Smirnov, Александр Георгиевич Смирнов, Smirnov, A. G.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #advanced mathematical theories #math-ph #math.FA #math.MP
paper · pdf · doi:10.48550/arxiv.math/0612756
8 pages
arxiv created 2006/12/25 · openalex publication_date 2006/12/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A convenient technique for proving kernel theorems for (LF)-spaces (countable inductive limits of Frechet spaces)is developed. The proposed approach is based on introducing a suitable modification of the functor of the completed inductive topological tensor product. Using such modified tensor products makes it possible to prove kernel theorems without assuming the completeness of the considered (LF)-spaces. The general construction is applied to proving kernel theorems for a class of spaces of entire analytic functions arising in nonlocal quantum field theory.