15. ÖMG-Kongress Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Sektion 9 - Reelle Analysis, Funktionalgleichungen
Dienstag, 18. September 2001, 17.00, Juristensitzungssaal

On covariant embeddings of a linear functional equation with respect to an analytic iteration group

Harald Fripertinger, Karl Franzens Universität Graz (Koautor: Ludwig Reich)

Let , , be formal power series in the indeterminate over (i.e. elements of the ring of such series), such that , and is embeddable into an analytic iteration group in . By a covariant embedding of the linear functional equation

(for the unknown series ) with respect to we understand families and with entire coefficient functions in , such that the system of functional equations and boundary conditions

holds for all solutions of and . We show how to solve the system (of so called cocycle equations) completely, describe when and how the boundary conditions and can be satisfied and present a large class of equations together with iteration groups for which there exist covariant embeddings of with respect to .

 E-Mail: harald.fripertinger@kfunigraz.ac.at Homepage: www-ang.kfunigraz.ac.at/~fripert/

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