Analytic Representations and Fourier Transforms of Analytic Functionals in $Z'$ Carried by the Real Space
Copyright policy )Analytic Representations and Fourier Transforms of Analytic Functionals in $Z'$ Carried by the Real Space
In the space $Z'$, the Fourier transform of the space $\mathcal{D}'$ of Schwartz-distributions, the notion of carrier is introduced. A characterization is given of all distributions $\mathcal{D}'$, the Fourier transform of which is carried by $\mathbb{R}^n $. Both, such distributions and the analytic functionals in $Z'$ carried by $\mathbb{R}^n $, are represented as sum of boundary values of holomorphic functions. This extends the case of tempered distributions which, regarded as elements of $Z'$, are obviously carried by $\mathbb{R}^n $.
Distributions and ultradistributions as boundary values of analytic functions, Paley-Wiener Theorem, Topological linear spaces of test functions, distributions and ultradistributions, Fourier Transform, Hyperfunctions, analytic functionals, Tempered Distributions, Distributional Boundary Values, Functions Holomorphic in Tubular Radial Domains, Entire Testfunctions, Analytic Functionals, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Algebraic Growth, Carrier of An Analytic Functional, Exponential Type
Distributions and ultradistributions as boundary values of analytic functions, Paley-Wiener Theorem, Topological linear spaces of test functions, distributions and ultradistributions, Fourier Transform, Hyperfunctions, analytic functionals, Tempered Distributions, Distributional Boundary Values, Functions Holomorphic in Tubular Radial Domains, Entire Testfunctions, Analytic Functionals, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Algebraic Growth, Carrier of An Analytic Functional, Exponential Type
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