On the form of homomorphisms into the differential group Ls 1 and their extensibility

Homomorphisms of the group $$L^1_s$$ into the group $$L^1_r$$ for r ≤ 3

“…Since L 1 1 ∼ = (R 0 , ·), the case s = 1 can be reduced to the determination of homomorphisms, in general, of an abelian group into L 1 r (cf. [4,5,6,9,10]) and therefore this case will not be discussed here. The case s = 2 and r = 2, 3 have been investigated in [1].…”

“…Even the simple case of homomorphisms from an abelian group into L 1 r leads to very complicated formulas (cf. [4,5,6]). …”

A new approach to the description of one-parameter groups of formal power series in one indeterminate

“…Case 1 and case 3 were already investigated in [6,7,9] using connections with the differential groups L 1 s (s ∈ N) and L 1 ∞ . These differential groups will not appear in the present paper.…”

The formal translation equation and formal cocycle equations for iteration groups of type I

“…(Let us mention here that, more generally, one may study homomorphisms θ from an abelian group (G, +) into Γ. This point of view is taken by W. Jab loński and L. Reich in [15], [16]. In the present paper we will only deal with the situation G = C.)…”

“…However, the explicit form and the universal character of these polynomials, but also possible relations among the involved additive and generalized exponential functions, remain still open. Only recently, the detailed structure of the coefficient functions was given in [15], [16] in the case when θ is a homomorphism from (G, +) into Γ 1 , that means if c 1 = 1, and in forthcoming papers for homomorphisms θ for which c 1 = 1.…”