English

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.

Keywords

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

R2 v1 2026-06-21T20:48:56.430Z