A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term

Details A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term

2012-04-13

arxiv.org/abs/1204.2924v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We discuss ordinary differential equations with delay and memory terms in Hilbert spaces. By introducing a time derivative as a normal operator in an appropriate Hilbert space, we develop a new approach to a solution theory covering integro-differential equations, neutral differential equations and general delay differential equations within a unified framework. We show that reasonable differential equations lead to causal solution operators.

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