Tempered Ultradistributions as Boundary Values of Analytic Functions

DOI10.2307/1999809zbMath0529.46031OpenAlexW4246415618MaRDI QIDQ3311130

Ram Shankar Pathak

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/1999809

zbMATH Keywords

tempered ultradistributionsdistributional boundary valueanalytic representation of distributionsfunctions analytic in tube domainsPaley-Wiener- Schwartz theoremsvacuum expectation values in quantum field theory

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Axiomatic quantum field theory; operator algebras (81T05) Hyperfunctions, analytic functionals (46F15) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Distributions and ultradistributions as boundary values of analytic functions (46F20)

Related Items (3)

A note on Fourier--Laplace transform and analytic wave front set in theory of tempered ultrahyperfunctions ⋮ Continuation of functionals on ultradifferentiable function spaces ⋮ Holomorphic extension theorem for tempered ultrahyperfunctions

Cites Work

• Darstellung der Schwartzschen Distributionen durch analytische Funktionen
• Almost analytic extension of ultradifferentiable functions and the boundary values of holomorphic functions
• Ultradistributions and quantum fields: Fourier-Laplace transforms and boundary values of analytic functions
• Distributional boundary values in the dual spaces of spaces of type \(\mathcal S\)
• Analytic functions and the Fourier transform of distributions. I, II
• Linear partial differential operators and generalized distributions
• Ultra-distributions definies sur \(R^ n\) et sur certaines classes de variétés différentiables
• Analytically Uniform Spaces and Some Applications
• Sur quelques extensions de la notion de distribution
• Analytic functions having distributional boundary values in W′-spaces
• Cauchy and Poisson integral representations for ultradistributions of compact support and distributional boundary values
• Analytic Representations and Fourier Transforms of Analytic Functionals in $Z'$ Carried by the Real Space
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