


On a
linear functional equation for formal power series. 
On a linear functional equation for formal power
series.
Jointly written with LUDWIG REICH.
Sitzungsberichte der Österreichischen
Akademie der Wissenschaften, Abt. II, 210:85134, 2001.
Abstract: Let ρ be a primitive j_{0} th
complex root of 1, C[[x]] the ring of formal power series in
x over ℂ, and let a(x), b(x) in C[[x]]. We study
the two equations
and
for φ in C[[x]], which occurred in connection with an
interesting and important special case when dealing with the
problem of a covariant embedding of (L) with respect to an
iteration group. (See H. Fripertinger and L. Reich.
On covariant embeddings of a linear
functional equation with respect to an analytic iteration
group.) We describe necessary and sufficient conditions for
finding nontrivial solutions of (L_{h}) and for finding
solutions of (L) in the form of "cyclic" functional equations for a
and b. Then we describe the set of all solutions of these
functional equations and present different representations of their
general solutions.
harald.fripertinger "at" unigraz.at, February 15,
2018






On a
linear functional equation for formal power series. 

