A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term
Classical Analysis and ODEs
2012-09-06 v3
Abstract
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.
Cite
@article{arxiv.1204.2924,
title = {A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term},
author = {Anke Kalauch and Rainer Picard and Stefan Siegmund and Sascha Trostorff and Marcus Waurick},
journal= {arXiv preprint arXiv:1204.2924},
year = {2012}
}
Comments
Minor adjustments done