On Hosszú’s functional equation in distributions
HTML articles powered by AMS MathViewer
- by E. L. Koh PDF
- Proc. Amer. Math. Soc. 120 (1994), 1123-1129 Request permission
Abstract:
In this paper, the Hosszú functional equation \[ f(x + y - xy) + g(xy) = h(x) + k(y)\] is reformulated in the domain of distributions. Its general solution is found which includes Fenyö’s solution as a special case.References
-
N. H. Abel, Über die Funktionen die der Gleichung $\phi x + \phi y = \phi (xfy + yfx)$ genug thun, J. Reine Angew. Math. 2 (1827), 386-394.
- J. Aczél, Grundriss einer allgemeinen Behandlung von einigen Funktionalgleichungstypen, Publ. Math. Debrecen 3 (1953), 119–132 (1954) (German). MR 62333
- J. Aczél, Lectures on functional equations and their applications, Mathematics in Science and Engineering, Vol. 19, Academic Press, New York-London, 1966. Translated by Scripta Technica, Inc. Supplemented by the author. Edited by Hansjorg Oser. MR 0208210 D. Hilbert, Mathematische probleme, Nachr. Ges. Wiss. Göttingen (1900), 253-297; Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, RI, 1976, p. 14.
- A. Járai, On regular solutions of functional equations, Aequationes Math. 30 (1986), no. 1, 21–54. MR 837038, DOI 10.1007/BF02189909
- A. Járai, Regularity properties of functional equations, Aequationes Math. 25 (1982), no. 1, 52–66. MR 716377, DOI 10.1007/BF02189597
- Halina Światak, On the regularity of the distributional and continuous solutions of the functional equations \[ \sum _{i=1}^{k}a_{l}(x,t)f(x+\varphi _{l}(t))= b(x,t)\], Aequationes Math. 1 (1968), 6–19. MR 279474, DOI 10.1007/BF01817554
- A. Tsutsumi and Sh. Haruki, The regularity of solutions of functional equations and hypoellipticity, Functional equations: history, applications and theory, Math. Appl., Reidel, Dordrecht, 1984, pp. 99–112. MR 954203, DOI 10.1007/978-94-009-6320-7_{1}0
- Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035, DOI 10.1007/978-3-642-96750-4
- Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, IX-X, Hermann, Paris, 1966 (French). Nouvelle édition, entiérement corrigée, refondue et augmentée. MR 0209834 I. Fenyö, Über eine lösungsmethode gewisser funktionalgleichungen, Acta Math. Hungar 7 (1957), 383-396.
- M. Neagu, About the Pompeiu equation in distributions, Inst. Politehn. Traian Vuia Timişoara Lucrăr. Sem. Mat. Fiz. May (1984), 62–66 (English, with Romanian summary). MR 783941
- John A. Baker, Functional equations, tempered distributions and Fourier transforms, Trans. Amer. Math. Soc. 315 (1989), no. 1, 57–68. MR 979965, DOI 10.1090/S0002-9947-1989-0979965-5
- John A. Baker, Functional equations, distributions and approximate identities, Canad. J. Math. 42 (1990), no. 4, 696–708. MR 1074230, DOI 10.4153/CJM-1990-036-1
- E. L. Koh, The Cauchy functional equations in distributions, Proc. Amer. Math. Soc. 106 (1989), no. 3, 641–646. MR 942634, DOI 10.1090/S0002-9939-1989-0942634-7
- E. Y. Deeba and E. L. Koh, The Pexider functional equations in distributions, Canad. J. Math. 42 (1990), no. 2, 304–314. MR 1051731, DOI 10.4153/CJM-1990-017-6
- E. Y. Deeba and E. L. Koh, d’Alembert functional equations in distributions, Proc. Amer. Math. Soc. 116 (1992), no. 1, 157–164. MR 1100648, DOI 10.1090/S0002-9939-1992-1100648-0
- E. Y. Deeba and E. L. Koh, Coupled functional equations in distributions, Indian J. Math. 33 (1991), no. 3, 275–285 (1992). MR 1335362
- I. Fenyő, On the general solution of a functional equation in the domain of distributions, Aequationes Math. 3 (1969), 236–246. MR 611691, DOI 10.1007/BF01817444 J. A. Baker, On a functional equation of Aczél and Chung, Aequationes Math, (to appear).
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 1123-1129
- MSC: Primary 39B52; Secondary 46F10
- DOI: https://doi.org/10.1090/S0002-9939-1994-1186990-8
- MathSciNet review: 1186990