


Covariant
embeddings of the linear functional equation with respect to an
iteration group in the ring of complex formal power
series 
Covariant embeddings of the linear functional equation with
respect to an iteration group in the ring of complex formal power
series
Jointly written with LUDWIG REICH.
Grazer Mathematische
Berichte 350, 96  121, 2006.
Abstract: Let a(x), b(x), p(x) be formal power series in
the indeterminate x over ℂ such that orda(x)=0, ordp(x)=1 and
p(x) is embeddable into an iteration group (π(s,x))_{s∈
ℂ} in C[[x]]. By a covariant embedding of the
linear functional equation
φ(p(x))=a(x)φ(x)+b (x), 
(L) 

(for the unknown series φ(x)∈ C[[x]]) with respect
to (π(s,x))_{s∈ ℂ} we understand families
(α(s,x))_{s∈ ℂ} and
(β(s,x))_{s∈ ℂ} of formal power series
which satisfy a system of cocycle equations and boundary conditions
such that
φ(π(s,x))=α(s,x)φ(x)+β(s,x),
s∈ ℂ, 
(Ls) 

holds true for all solutions φ of (L). In this paper we present
a complete solution of this problem and we demonstrate how earlier
results concerning covariant embeddings with respect to analytic
iteration groups can be derived from these more general results.
harald.fripertinger "at" unigraz.at, October 12,
2017






Covariant
embeddings of the linear functional equation with respect to an
iteration group in the ring of complex formal power
series 

