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On the Behavior of Power Series with Completely Additive Coefficients

Petrushov O.

Bulletin of the Polish Academy of Sciences. Mathematics

2015

Vol. 63, no. 3

217--225

Consider the power series A(z)=∑∞n=1 α (n) zn, where α(n) is a completely additive function satisfying the condition α(p) = o(lnp) for prime numbers p. Denote by e(l/q) the root of unity e2πil/q. We give effective omega-estimates for A(e(l/pk)r) when r→1−. From them we deduce that if such a series has non-singular points on the unit circle, then it is a zero function.

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.

A comparison of some conditional functional equations

Chmieliński J.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

Vol. 45, [Z] 2

137--144

For real inner product spaces we consider and compare the classes of mappings satisfying some conditional and unconditional functional equations.