Results 61 to 70 of about 101 (82)

THE SPACE OF FOURIER HYPERFUNCTIONS AS AN INDUCTIVE LIMIT OF HILBERT SPACES

Communications of the Korean Mathematical Society, 2004
Summary: We research properties of the space of measurable fun-ctions square integrable with weight \(\exp(2\nu|x|)\), and those of the space of Fourier hyperfunctions. Also we show that the several embedding theorems hold true, and that the Fourier-Lapace operator is an isomorphism of the space of strongly decreasing Fourier hyperfunctions onto the ...
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Quasiasymptotic behavior of Fourier hyperfunctions

Theoretical and Mathematical Physics(Russian Federation), 1980
V V Zharinov
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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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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, Kwang Whoi Kim, Eun Gu Lee
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Schwartz’ Kernel Theorem for Fourier Hyperfunctions

2000
An appropriate general version of the kernel theorem of L. Schwartz is formulated for Fourier hyperfunctions and a direct functional analytic proof is presented. This talk is based on a joint paper [2] with S. Nagamachi.
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Vector-valued Fourier hyperfunctions [PDF]

, 2014
This work is dedicated to the development of the theory of Fourier hyperfunctions in one variable with values in a non-necessarily metrizable locally convex space E. Moreover, necessary and sufficient conditions are described such that a reasonable theory of E-valued Fourier hyperfunctions exists.
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Microlocalization within Some Classes of Fourier Hyperfunctions

2006
New presheaves of hyperfunction spaces with the growth estimates with respect to |x| → ∞ and y → 0 in a cone Γ are introduced. Then it is shown that the Laplace transform is a bijective mapping of the space of tempered ultradistributions on R n of non-quasianalytic class onto the corresponding hyperfunction space of sections over D n, the ...
Richard D. Carmichael, Atsuhiko Eida, Stevan Pilipović   +2 more
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Mehler kernel approach to Fourier ultra-hyperfunctions

Complex Variables and Elliptic Equations, 2022
Masanori Suwa
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Extension of Sato's hyperfunctions

Functiones Et Approximatio, Commentarii Mathematici, 2011
Michael Langenbruch
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