The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (1265 KB) | Metadata | Table of Contents | ZAA summary
Volume 17, Issue 2, 1998, pp. 339–360
DOI: 10.4171/ZAA/826

Published online: 1998-06-30

On the Solvability of Linear Differential Equations with Unbounded Operators in Banach Spaces

E.A. Barkova[1] and P. P. Zabrejko[2]

(1) Belgos University, Minsk, Belarus
(2) The Academy of Sciences of Belarus, Minsk, Belarus

This article deals with some solvability results on the Cauchy problem for linear differential equations with unbounded operators. The main result consists in the description of the set of initial data for which the corresponding solutions are represented by means of the classical exponential formula in the stationary case, and by means of the Peano matriciant formula in the non-stationary case. In this connection a new generalization of Gelfand’s lemma about analytic vectors of the generator of a strongly continuous group is proved.

Keywords: Banach spaces, linear differential equations with unbounded operators, abstract Cauchy problems, Roumieu spaces, Gevrey spaces, Beurling spaces

Barkova E.A., Zabrejko P. P.: On the Solvability of Linear Differential Equations with Unbounded Operators in Banach Spaces. Z. Anal. Anwend. 17 (1998), 339-360. doi: 10.4171/ZAA/826