THE STUDY OF HYPERFUNCTION QUANTUM FIELD THEORY

In the paper "Hyperfunction quantum field theory : Analytic structure, modular aspects, and local observable algebras" by S. Nagamachi and E. Bruning, the net of local observable algebras is constructed in the theory of hyperfunction quantum field, which plays an important role in the theory of Haag-Araki. Special technique is required in the hyperfunction quantum field theory because test-functions with compact supports which are used in standard tempered quantum field theory are not available in the hyperfunction quantum field theory.In the paper "SUPPORT AND KERNEL THEOREM FOR FOURIER HYPERFUNCTIONS" by T. Nishimura and S. Nagamachi the kernel theorem with support conditions is proved for Fourier hyperfunctions, using the method of complexanasysis in several variables. In the paper "Kernel Theorem for Fourier Hyperfunctions" by E. Bruning and S. Nagamachi the same result is proved in another method, the method of functional analysis.In the paper "Hyperfunction quantum field ; theory : Localized fields without localized test functions" by S. Nagamachi and E. Bruning a model which satisfies all the axioms of hyperfunction quantum field theory, and has no test-functions of compact supports.

In the paper "Hyperfunction quantum field theory : Analytic structure, modular aspects, and local observable algebras" by S. Nagamachi and E. Bruning, the net of local observable algebras is constructed in the theory of hyperfunction quantum field, which plays an important role in the theory of Haag-Araki. Special technique is required in the hyperfunction quantum field theory because test-functions with compact supports which are used in standard tempered quantum field theory are not available in the hyperfunction quantum field theory.In the paper "SUPPORT AND KERNEL THEOREM FOR FOURIER HYPERFUNCTIONS" by T. Nishimura and S. Nagamachi the kernel theorem with support conditions is proved for Fourier hyperfunctions, using the method of complexanasysis in several variables. In the paper "Kernel Theorem for Fourier Hyperfunctions" by E. Bruning and S. Nagamachi the same result is proved in another method, the method of functional analysis.In the paper "Hyperfunction quantum field ; theory : Localized fields without localized test functions" by S. Nagamachi and E. Bruning a model which satisfies all the axioms of hyperfunction quantum field theory, and has no test-functions of compact supports.