Snakes and articulated arms in an Hilbert space
Fernand Pelletier, Rebiha Saffidine

TL;DR
This paper illustrates advanced results on integrability and accessibility of vector field distributions in Banach and Hilbert spaces, generalizing finite-dimensional theorems to infinite-dimensional settings.
Contribution
It extends finite-dimensional accessibility theorems to separable Hilbert spaces using Banach manifold techniques and prior integrability results.
Findings
Generalization of a finite-dimensional accessibility theorem to Hilbert spaces
Illustration of integrability of distributions on Banach manifolds
Application of previous results to infinite-dimensional Hilbert space context
Abstract
The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [Pe] and [LaPe]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [Ha], [Ro] and proved for a finite dimensional Hilbert space
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Taxonomy
TopicsAdvanced Banach Space Theory · Holomorphic and Operator Theory · Nonlinear Differential Equations Analysis
