 |
 |
 |
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" uni-graz.at, August 27,
2026
|
|
|
 |
 |
 |
GDPR |
Covariant
embeddings of the linear functional equation with respect to an
iteration group in the ring of complex formal power
series |
 |
 |
