Results 1 to 10 of about 222 (115)
Numerical calculation of Fourier transforms based on hyperfunction theory
Journal of Computational and Applied Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hidenori Ogata
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A Characterization for Fourier Hyperfunctions
Publications of the Research Institute for Mathematical Sciences, 1994 The space of test functions for Fourier hyperfunctions is characterized by two conditions \sup |φ (x)| \exp k|x|<∞ and \sup|\hat φ(ξ) | \exp h|ξ|<∞ for some
Chung, Jaeyoung +2 more
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Periodic hyperfunctions and Fourier series [PDF]
Proceedings of the American Mathematical Society, 1999 Every periodic hyperfunction is a bounded hyperfunction and can be represented as an infinite sum of derivatives of bounded continuous periodic functions. Also, Fourier coefficients c
Chung, Soon-Yeong +2 more
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Structure of the extended Fourier hyperfunctions
Japanese journal of mathematics. New series, 1993 \textit{T. Matsuzawa's} Methode zur Beschreibung der Struktur von Räumen von Distributionen, Ultradistributionen und Hyperfunktionen [Trans. Am. Math. Soc. 313, No. 2, 619-654 (1989; Zbl 0681.46042)] wird hier zur Strukturbeschreibung des Raumes \({\mathcal G}'\) von erweiterten Fourier Hyperfunktionen verwendet. Es wird gezeigt, daß jedes \(u\) in \({\
CHUNG, Soon-Yeong +2 more
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Fourier hyperfunctions of general type
Kyoto Journal of Mathematics, 1988 The author studies vector valued Fourier hyperfunctions valued in a complex Hilbert space \(H\) which is not necessarily separable. This is a direct generalization of the author and \textit{Sh. Nagamachi} [Proc. Japan Acad. 51, 558-561 (1975; Zbl 0333.46031) and J. Math., Tokushima Univ. 9, 1-33 (1975; Zbl 0315.46039)]. He realizes \(H\)-valued Fourier
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CONVOLUTORS FOR THE SPACE OF FOURIER HYPERFUNCTIONS
Journal of the Korean Mathematical Society, 2005 The author of this paper defines the convolution of Fourier hyperfunctions and analyses its properties making use of the method given in the book [\textit{S. G. Gindikin} and \textit{L. R. Volevich}, ``Distributions and Convolution Equations'' (Gordon and Breach Sci. Publ.) (1992; Zbl 0760.46029)].
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Convergence in the space of Fourier hyperfunctions
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pilipović, Stevan, Stanković, Bogoljub
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Fundamental Properties of Modified Fourier Hyperfunctions
Tokyo Journal of Mathematics, 1985 There are three types of (vector-valued) Fourier hyperfunctions: classical (1960, 1975), modified (1976) and of mixed type (1981). The sheaves of these three types of Fourier hyperfunctions are defined on \(D^ n\), the radial compactification of \(R^ n\), all three of them are flabby, and each space of global sections of sheaves is stable under Fourier
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Quantum Field Theory in Terms of Fourier Hyperfunctions
Publications of the Research Institute for Mathematical Sciences, 1976 The Wightman axioms are extended to the quantum field theory in terms of Fourier hyperfunctions. The support concept of hyperfunctions is crucial for the formulation of locality and spectral condition. The complete equivalence is proved between modified Wightman axioms for relativistic theory and modified Osterwalder–Schrader axioms for Euclidean ...
Nagamachi, Shigeaki +1 more
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Schwartz kernel theorem for the Fourier hyperfunctions
Tsukuba Journal of Mathematics, 1995 The purpose of this paper is to give a direct proof of the Schwartz kernel theorem for the Fourier hyperfunctions. The Schwartz kernel theorem for the Fourier hyperfunctions means that with every Fourier hyperfunction \(K\) in \({\mathcal F}(\mathbb{R}^{n_1}\times \mathbb{R}^{n_2})\) we can associate a linear map \[ {\mathcal K}:{\mathcal F}(\mathbb{R}^
Chung, Soon-Yeon +2 more
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