On stability of linear periodic differential difference equations

The paper considers the equation where the operator-valued bounded functions a j and b j are 2π-periodic, and the operator-valued kernels m and n are 2π-periodic with respect to the first argument. The connection between the input-output stability of the equation and the invertibility of a family of...

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Bibliographic Details
Published in:Quaestiones mathematicae 2018-05, Vol.41 (4), p.565-584
Main Authors: Kurbatov, V.G., Kuznetsova, V.I.
Format: Article
Language:English
Subjects:
causal invertibility
delay
Difference equations
differential difference equation
Differential equations
differential operator
functional differential equation
Operators (mathematics)
Periodic functions
Stability
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Summary:The paper considers the equation where the operator-valued bounded functions a j and b j are 2π-periodic, and the operator-valued kernels m and n are 2π-periodic with respect to the first argument. The connection between the input-output stability of the equation and the invertibility of a family of operators acting on the space of periodic functions is investigated.
ISSN:1607-3606
1727-933X
DOI:10.2989/16073606.2017.1393470