Functional equations for homogeneous polynomials arising from multilinear mappings and their stability
Abstract
Some characterizations of homogeneous polynomials and of polynomials in general are given. This is done not only in the usual case but also for vector spaces over non archimedean valued fields. Moreover stability results in connection with these characterizations are given.
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2. W.A. Beyer, Approximately Lorentz transformations and p-adic fields, preprint, Los Alamos National Laboratory (1986), LA-DC-9486.
3. D.Ž. Djoković, A representation theorem for (X_1 - 1)(X_2 - 1)...(X_n - 1) and its applications, Ann. Polon. Math. 22 (1969), 189-198.
4. K.J. Heuvers, Functional equations which characterize n-forms and homogeneous functions of degree n, Aequationes Math. 22 (1981), 223-248.
5. M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Uniwersytet Śląski, PWN, Warszawa - Kraków - Katowice, 1985.
6. W.H. Schikhof, Ultrametric calculus - An introduction to p-adic analysis, Cambridge studies in advanced mathemathics 4, Cambridge University Press, Cambridge-London, 1984.
7. J. Schwaiger, A generalized polarization formula for homogeneous polynomials, in: Reich, L. (ed.), VI. Mathematikertreffen Zagreb-Graz, Opatija, Grazer Mathematische Berichte, Ber. 304 (1989), 111-117.
8. J. Schwaiger, Report of Meeting (The 30-th Symposium on Functional Equations), 10. Remark, Aequationes Math. 48 (1993), 289.
9. J. Tabor, On approximately linear mappings, Publ. Math. Debrecen (to appear).
SchwaigerJ. (1994). Functional equations for homogeneous polynomials arising from multilinear mappings and their stability. Annales Mathematicae Silesianae, 8, 157-171. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14232
Jens Schwaiger
Institut für Mathematik, Universität Graz, Austria Austria
Institut für Mathematik, Universität Graz, Austria Austria
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