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

Е. А. Баркова | Zendy; Petr P. Zabrejko | Zendy

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

Author(s) -

Е. А. Баркова,

Petr P. Zabrejko

Publication year - 1998

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/826

Subject(s) - unbounded operator , mathematics , c0 semigroup , banach space , linear operators , finite rank operator , operator theory , pure mathematics , mathematical analysis , bounded function

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.

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