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http://dx.doi.org/10.4134/BKMS.2011.48.2.387

ON THE INITIAL VALUES OF SOLUTIONS OF A GENERAL FUNCTIONAL EQUATION  

Chung, Jae-Young (Department of Mathematics Kunsan National University)
Kim, Do-Han (Department of Mathematics Seoul National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.2, 2011 , pp. 387-396 More about this Journal
Abstract
We consider a general functional equation with time variable which arises when we investigate regularity problems of some general functional equations. As a result we prove the regularity of the initial values of the solutions. Also as an application we prove the regularity of solutions of some classical functional equations and their distributional versions.
Keywords
unctional equation; convolution; generalized function; heat kernel;
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1 J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, Cambridge, 1989.
2 J. Aczel and J. K. Chung, Integrable solutions of functional equations of a general type, Studia Sci. Math. Hungar. 17 (1982), no. 1-4, 51-67.
3 J. M. Speiser, H. J. Whitehouse, and N. J. Berg, Signal processing architectures using convolutional technology, Real time Signal Processing, SPIE 154 (1978), 66-80.
4 L. Szekelyhidi, The stability of the sine and cosine functional equations, Proc. Amer. Math. Soc. 110 (1990), no. 1, 109-115.   DOI
5 L. Szekelyhidi, On the Levi-Civita Functional Equation, Forschungszentrum Graz, Mathematisch-Statistische Sektion, Graz, 1988.
6 J. Chung, A distributional version of functional equations and their stabilities, Nonlinear Anal. 62 (2005), no. 6, 1037-1051.   DOI   ScienceOn
7 J. Chang and J. Chung, The stability of the sine and cosine functional equations in Schwartz distributions, Bull. Korean Math. Soc. 46 (2009), no. 1, 87-97.   과학기술학회마을   DOI   ScienceOn
8 J. Chung, A functional equation of Aczel and Chung in generalized functions, Adv. Difference Equ. 2008 (2008), Art. ID 147979, 11 pp.
9 J. Chung, Stability of approximately quadratic Schwartz distributions, Nonlinear Anal. 67 (2007), no. 1, 175-186.   DOI   ScienceOn
10 J. Chung, S.-Y. Chung, and D. Kim, Generalized Pompeiu equation in distributions,Appl. Math. Lett. 19 (2006), no. 5, 485-490.   DOI   ScienceOn
11 E. Y. Deeba, E. L. Koh, P. K. Sahoo, and S. Xie, On a distributional analog of a sum form functional equation, Acta Math. Hungar. 78 (1998), no. 4, 333-344.   DOI
12 E. Deeba, P. K. Sahoo, and S. Xie, On a class of functional equations in distribution, J. Math. Anal. Appl. 223 (1998), no. 1, 334-346.   DOI   ScienceOn
13 E. Y. Deeba and S. Xie, Distributional analog of a functional equation, Appl. Math.Lett. 16 (2003), no. 5, 669-673.   DOI   ScienceOn
14 L. Schwartz, Theorie des distributions, Hermann, Paris, 1966.
15 I. M. Gelfand and G. E. Shilov, Generalized Functions. II, Academic Press, New York, 1968.
16 L. Hormander, The Analysis of Linear Partial Differential Operators. I, Springer-Verlag, Berlin-New York, 1983.
17 A. Jarai, A remark to a paper of J. Aczel and J. K. Chung, Studia Sci. Math. Hungar. 19 (1984), no. 2-4, 273-274.