Results 1 to 10 of about 83 (67)
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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On localization properties of Fourier transforms of hyperfunctions
Journal of Mathematical Analysis and Applications, 2009 21 pages, final version, accepted for publication in J. Math.
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DENSENESS OF TEST FUNCTIONS IN THE SPACE OF EXTENDED FOURIER HYPERFUNCTIONS [PDF]
Bulletin of the Korean Mathematical Society, 2004 Let \(F_{(h,\nu)}\) be the space of differentiable functions \(\varphi(x)\) for which some sup-norm is finite. Then one has the continuous embedding \(F_{(h,\nu)}\subset F_{(h',\nu')}\), \(h\geq h'>0, \nu\geq\nu'\). Let \(\mathcal G=\bigcap_{h,\nu}F_{(h,\nu)}\) be endowed with the natural projective topology.
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Stability of Trigonometric Functional Equations in Generalized Functions
Journal of Inequalities and Applications, 2010 We consider the Hyers-Ulam stability of a class of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.
Jeongwook Chang, Jaeyoung Chung
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Stability of Quartic Functional Equations in the Spaces of Generalized Functions
Advances in Difference Equations, 2009 We consider the general solution of quartic functional equations and prove the Hyers-Ulam-Rassias stability. Moreover, using the pullbacks and the heat kernels we reformulate and prove the stability results of quartic functional equations in the spaces ...
Chung Soon-Yeong, Lee Young-Su
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Negative Powers of Contractions Having a Strong AA+ Spectrum
Moroccan Journal of Pure and Applied Analysis, 2023 Zarrabi proved in 1993 that if the spectrum of a contraction T on a Banach space is a countable subset of the unit circle 𝕋, and if limn→+∞log(‖T−n‖)n=0{\lim _{n \to + \infty }}{{\log \left( {\left\| {{T^{ - n}}} \right\|} \right)} \over {\sqrt n ...
Esterle Jean
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Stability of a Quadratic Functional Equation in the Spaces of Generalized Functions
Journal of Inequalities and Applications, 2008 Making use of the pullbacks, we reformulate the following quadratic functional equation: in the spaces of generalized functions. Also, using the fundamental solution of the heat equation, we obtain the general solution and prove the Hyers-Ulam ...
Lee Young-Su
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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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Stability of Cubic Functional Equation in the Spaces of Generalized Functions
Journal of Inequalities and Applications, 2007 In this paper, we reformulate and prove the Hyers-Ulam-Rassias stability theorem of the cubic functional equation f(ax+y)+f(ax−y)=af(x+y)+af(x−y)+2a(a2−1)f(x) for fixed integer a with a≠0,±1 in the spaces of Schwartz tempered
Soon-Yeong Chung, Young-Su Lee
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