C-admissibility and analytic \(C\)-semigroups (Q555105)
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scientific article; zbMATH DE number 5930968
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | C-admissibility and analytic \(C\)-semigroups |
scientific article; zbMATH DE number 5930968 |
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C-admissibility and analytic \(C\)-semigroups (English)
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22 July 2011
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This paper gives a uniqueness result for the solution of the operator equation \(AX-XB=CD\) in the case of \(A\) being the generator of an analytic \(C\)-regularized semigroup in a Banach space \(F\) and \(B\) being a closed linear operator in \(F\) with some further properties. When \(C=I\), the result was proved by \textit{Q. P. Vu} and \textit{E. Schüler} in [J. Differ. Equations 145, No. 2, 394--419 (1998; Zbl 0918.34059)].
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operator equation
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analytic \(C\)-regularized semigroups
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uniqueness
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