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The local structure of the solutions of the multidimensional translation equation

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Summary

The general solution of the multidimensional translation equation, which was considered by J. Aczél, L. Berg and Z. Moszner under conditions guaranteeing that it exists globally, is considered here locally, under certain differentiability conditions.

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References

  1. Aczél, J.,Lectures on functional equations and their applications. Academic Press, New York, 1966.

    Google Scholar 

  2. Aczél, J., Berg, L. etMoszner, Z.,Sur l'équation de translation multidimensionnelle. Resultate Math.19 (1991), 195–210.

    Google Scholar 

  3. Aczél, J. andHosszú, M.,On transformations with several parameters and operations in multidimensional spaces. Acta Math. Acad. Sci. Hungar.7 (1956), 327–338.

    Google Scholar 

  4. Deeba, E. Y. andKoh, E. L.,The Pexider functional equations in distributions. Canad. J. Math.42 (1990), 304–314.

    Google Scholar 

  5. Förg-Rob, W.,On differentiable solutions of the translation equation. [Ber. Math.-Statist. Sekt. Forschungsgesellsch. Joanneum, Nr. 287]. Forschungszentrum, Graz, 1988.

    Google Scholar 

  6. Gronau, D.,On the structure of the solutions of the Jabotinsky equation in Banach spaces. Z. Anal. Anw. (to appear).

  7. Moszner, Z.,Structure de l'automate plein, réduit et invertible. Aequationes Math.9 (1973), 46–59.

    Article  Google Scholar 

  8. Moszner, Z.,Une généralization d'un résultat de J. Aczél et M. Hosszú sur l'équation de translation. Aequationes Math.37 (1989), 267–278.

    Article  Google Scholar 

  9. Ng, C. T.,Inverse systems and their translation equation on topological spaces. Acta Math. Acad. Sci. Hungar.31 (1978), 227–232.

    Article  Google Scholar 

  10. Radó, F. andBaker, J. A.,Pexider's equation and aggregation of allocations. Aequationes Math.32 (1987), 227–239.

    Google Scholar 

  11. Riesz, F. etSz.-Nagy, B.,Leçons d'analyse fonctionnelle. Akadémiai Kiadó, Budapest, 1953.

    Google Scholar 

  12. Sibirsky, K. S.,Introduction to topological dynamics. Noordhoff Int. Publ., Leyden, 1975.

    Google Scholar 

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Authors and Affiliations

  1. Universität Rostock, Fachbereich Mathematik, Universitätsplatz I, D-18055, Rostock, Germany

    Lothar Berg

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  1. Lothar Berg
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Berg, L. The local structure of the solutions of the multidimensional translation equation. Aeq. Math. 46, 164–173 (1993). https://doi.org/10.1007/BF01834005

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  • DOI: https://doi.org/10.1007/BF01834005

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