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On the initial values of solutions of a general functional equation

김도한|정재영
대한수학회 (The Korean Mathematical Society)|2011.03|대한수학회보 (Bulletin of the KMS)|제48권 제2호|pp. 387-396

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참고문헌

키워드

functional equationconvolutionheat kernelgeneralized function
주제분류수학

초록

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.

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.

참고문헌 (17)

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  3. Jeongwook Chang, "The stability of the sine and cosine functional equations in Schwartz distributions", 대한수학회보, 46(1), pp.87~97 (2009), 대한수학회
  4. J. Chung, "A functional equation of Aczel and Chung in generalized functions", Adv. Difference Equ, pp.11~ (2008)
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  11. I. M. Gelfand, "Generalized Functions. II" (1968), Academic Press
  12. L. Hormander, "The Analysis of Linear Partial Differential Operators. I" (1983), Springer-Verlag
  13. A. Jarai, "A remark to a paper of J. Aczel and J. K. Chung", Studia Sci. Math. Hungar, 19(2), pp.273~274 (1984)
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  15. J. M. Speiser, "Signal processing architectures using convolutional technology", Real time Signal Processing, SPIE, 154, pp.66~80 (1978)
  16. L. Szekelyhidi, "The stability of the sine and cosine functional equations", Proc. Amer. Math. Soc, 110(1), pp.109~115 (1990)
  17. L. Szekelyhidi, "On the Levi-Civita Functional Equation, Forschungszentrum Graz" (1988), Mathe- matisch-Statistische Sektion

관련 논문AI추천

HYPERSTABILITY OF THE GENERAL LINEAR FUNCTIONAL EQUATIONMagdalena Piszczek대한수학회 · 대한수학회보2015 · 제52권 제6호STABILITY OF TRIGONOMETRIC TYPE FUNCTIONAL EQUATIONS IN RESTRICTED DOMAINS정재영한국수학교육학회 · 이론수학과 교직수학2011 · 제18권 제3호Regularity for semilinear retarded functional integrodifferential equations정진문, 천수진대한수학회 · 대한수학회논문집2013 · 제28권 제3호A characterization of Sobolev spaces by solutions of heat equation and a stability problem for a functional equation권덕용, 이영수, 정순영, 정윤성대한수학회 · 대한수학회논문집2008 · 제23권 제3호On the Stability of Functional Equations in $n$-variables and its applicationsGwang Hui Kim대한수학회 · 대한수학회논문집2005 · 제20권 제2호The stability of the sine and cosine functional equations in Schwartz distributions정재영, Jeongwook Chang대한수학회 · 대한수학회보2009 · 제46권 제1호

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