Enumeration of non-isomorphic canons Publications, to be read On covariant embeddings of a linear functional equation with respect to an analytic iteration group in some non-generic cases. 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, 210:85-134, 2001.

Abstract: Let ρ be a primitive j0 -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

φ(ρx)=a(x)φ(x)+b(x) (L)

and

φ(ρx)=a(x)φ(x) (Lh)

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. Accepted for publication in the International Journal of Bifurcation and Chaos.) We describe necessary and sufficient conditions for finding nontrivial solutions of (Lh) 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" uni-graz.at, January 12, 2012

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