Analytic Representations and Fourier Transforms of Analytic Functionals in $Z'$ Carried by the Real Space

DOI10.1137/0509081zbMath0406.46033OpenAlexW2151586618MaRDI QIDQ4192524

J. W. de Roever

Publication date: 1978

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0509081

zbMATH Keywords

Paley-Wiener TheoremFourier TransformTempered DistributionsExponential TypeAlgebraic GrowthAnalytic FunctionalsCarrier of An Analytic FunctionalDistributional Boundary ValuesEntire TestfunctionsFunctions Holomorphic in Tubular Radial Domains

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Hyperfunctions, analytic functionals (46F15) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Distributions and ultradistributions as boundary values of analytic functions (46F20)

Related Items (8)

Integral transforms of generalized functions ⋮ On a space of smooth functions on a convex unbounded set in \(\mathbb R^{n }\) admitting holomorphic extension in \(\mathbb C^{n }\) ⋮ Various kinds of sensitive singular perturbations ⋮ Analytic functions having distributional boundary values in W′-spaces ⋮ A theorem of Paley-Wiener type for ultradistributions ⋮ SENSITIVE VERSUS CLASSICAL SINGULAR PERTURBATION PROBLEM VIA FOURIER TRANSFORM ⋮ Tempered Ultradistributions as Boundary Values of Analytic Functions ⋮ Cauchy and Poisson integral representations for ultradistributions of compact support and distributional boundary values

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