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We prove in this paper that stability of the translation equation in the ring of formal power series K½½X (more precisely, in the group of invertible formal series over K )i s equivalent to some kind of extensibility of one-parameter groups of truncated formal power series. From this we deduce the stability of the translation equation in K½½X .

sitzungsberichte. abteilung ii, mathematische, physikalische und technische wissenschaften/sitzungsberichte/sitzungsberichte und anzeiger der mathematisch-naturwissenschaftlichen klasse

Stability of the Translation Equation in Rings of Formal Power Series and Partial Extensibility of One-Parameter Groups of Truncated Formal Power Series