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Polynomials in additive functions and generalized polynomials

Schwaiger J., Prager W.

Demonstratio Mathematica

2008

Vol. 41, nr 3

589-613

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.