Polynomials in additive functions and generalized polynomials

• Autorzy: Schwaiger J. , Prager W.
• Języki publikacji: EN

Abstrakty

EN

We consider polynomials P in additive functions g1,... , gm and present two approaches for a characterization of those generalized polynomials p, which may be represented as p = P o (g1,..., gm). Under rather general assumptions on the domains of the gi and of P, one of the approaches is based on certain properties of subspaces generated by translates of p. The other approach utilizes the fact, that every p is the diagonalization of an associated multi-Jensen function.

Słowa kluczowe

EN

polynomials; generalized polynomials; additive functions; multi-Jensen functions

PL

wielomiany; wielomiany ogólne; funkcje addytywne; funkcje Jensena

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 3
• Strony: 589--613
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Schwaiger J.

autor

Prager W.

• Institut fur Mathematik und Wissenschaftliches Rechnen Karl-Franzens Universitat Graz A-8010 Graz, Austria,

Bibliografia

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• [6] W. Prager, J. Schwaiger, Multi-affine and multi-Jensen functions and their connection with generalized polynomials, Aequationes Math. 69 (2005), 41-57.
• [7] L. Reich, Oral Communication, Graz 2004.
• [8] L. Reich, J. Schwaiger, On polynomials in additive and multiplicative functions, In: Aczél, J. (Ed.), Functional Equations: History, Applications and Theory, D. Reidel Publishing Company, Dordrecht etc. 1984.
• [9] L. Székelyhidi, Convolution Type Functional Equations on Topological Abelian Groups, World Scientific, Singapore 1991.