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Edge of the Wedge Theorem for Fourier Hyperfunctions

Edge of the Wedge Theorem for Fourier Hyperfunctions
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Schwartz kernel theorem for the Fourier hyperfunctions

Schwartz kernel theorem for the Fourier hyperfunctions
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Analytic fourier hyperfunctions

Applicable Analysis, 1999
It is proved first a generalized Painleve's theorem to be used to prove necessary and sufficient conditions that a Fourier hyperfunction is defined by a real analytic function. These results are applied to the Taylor asymptotic expansion for Fourier hyperfunctions.
Bogoljub Stanković
exaly   +2 more sources

Convolution and multiplication operators in Fourier hyperfunctions

Integral Transforms and Special Functions, 2006
We characterize the multiplication and convolution operators in the space ℱ′ of Fourier hyperfunctions. This generalizes the results of Schwartz on the multiplication and convolution operators on the space 𝒮′ of tempered distributions to the space ℱ′ of Fourier hyperfunctions.
Dohan Kim
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Fourier analysis, distributions and hyperfunctions

Integral Transforms and Special Functions, 1998
The theory of hyperfunctions and Fourier hyperfunctions is a really natural extension of the Schwartz theory of distributions and tempered distributions. We show that the naturalness of hyperfunctions comparing our results in hyperfunctions and the corresponding results in distributions in such areas as the characterization of test function spaces in ...
Jaeyoung Chung, Soon-Yeong Chung, Dohan Kim   +2 more
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Edge of the wedge theorem for Fourier hyperfunctions

Funkcialaj Ekvacioj, 1993
Let \(D^ n= \mathbb{R}^ n\cup S_ \infty^{n-1}\) denote the radial compactification of \(\mathbb{R}^ n\). If \(X\) is an open subset of \(D^ n\) then \(R(X)\) stands for the set of all Fourier hyperfunctions on \(X\). If \(\Gamma\) is a cone in \(\mathbb{R}^ n \setminus \{0\}\) then \(\Gamma^ 0\) is defined as the set \(\{\omega\in \mathbb{R}^ n\mid ...
Nagamachi, Shigeaki, Nishimura, Takeshi
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Wiener-Type Tauberian Theorems for Fourier Hyperfunctions

Zeitschrift für Analysis und ihre Anwendungen, 2002
Two Wiener-type Tauberian theorems concerning Fourier hyperfunctions are proved and commented. It is shownt that the shift asymptotics ( S -asymptotics) of a hyperfunction f is determined by the ordinary asymptotics of
Pilipović, Stevan, Stanković, Bogoljub
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Periodic Hyperfunctions and Fourier Series Fourier Series

1992
We have now almost finished the general discussion of hyperfunctions. From now on we shall attempt to apply this general theory to various cases. In this chapter we study periodic hyperfunctions. Then we shall see that the theory of Fourier series is naturally absorbed into the theory of Fourier transformations.
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The structure of a convergent family of fourier hyperfunctions

Integral Transforms and Special Functions, 1998
We give the structural properties of a family of Fourier hyper-functions which converges as . The main result is also given in [5] but here we give an extended version with all the details of the proofs.
S. Pilipovlć, B. Stanković
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Asymptotic Taylor expansion for Fourier hyperfunctions

Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1997
Summary: A necessary and sufficient condition is proved that the asymptotic Taylor expansion for a Fourier hyperfunction converges in the space of Fourier hyperfunctions.
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